I'm no good with writing events, but I could help you at least get the gist of how they'd work. For example, just throwing somethings out;
1. Alban secedes from Scotland due to Anglicization
A Gaelic Alban would, if violently seceding, ally itself, or even submit itself (could have an event for it, giving them the option to become an ally, or become a vassal, recieving perhaps a slight population boost as Gaelic lords in Ireland resettle in Scotland amongst their new subjects, or getting a small token gift from Ireland, but gives Ireland cores in their provinces {assuming Ireland doesn't have them already from claiming rights to their lands}) to Eire. This would be for more pragmatic reasons than anything; Eire is a Gaelic power that'd be sympathetic to them; at least more sympathetic than others. Eire may also have an event series tied to the Anglicization of Scotland; essentially funding highland rebellions. A successful rebellion that seizes the Highlands and Grampians becomes Alban.
Once at peace, they may pursue claims on the remainder of Scottish lands because, in their eyes, they're the proper rulers of the kingdom; they didn't really 'secede', so much as reassert their authority; Gaels founded the kingdom, so, they would reason, they have legal ownership of those lands, and could recieve cores in them, but end up, again, at war with the Scots (unless they Scots were defeated and those lands are already under Alban's control, in which case they should get cores in them anyway). However, Alban could softball this move, claiming solely ownership over former Pictish lands and Strathclyde, and recognize the other Scots as a seperate entity; avoids war, but no additional cores (except possibly Strathclyde, if that's become Inglis). That is, essentially, recognizing what was once all Celtic Alba (Gaelic and Brythonic, though Strathclyde would become ostensibly Gaelic, and would be already by this point), and discludes Inglis Lothian.
Alban now has the right to make a legal bid for power in Ireland itself, once it has local affairs settled. This has one of three options. The first being to let any claim drop for the sake of peace (improved relations with Ireland). The second is to lay claim on Ulster; the Ui Neill drove the Dalriatta out of Ireland from here, and some lands there should be under their legal ownership once reunited with Ireland (damages relationship, but not war; gives a core in Ulster, gives Ireland the option of ceding Ulster to Alban to greatly improve relations, or ignore their claim, damaging relations further; possibly also allow a declaration of war, and recieving cores on Alban's provinces for Ireland, if they haven't already). The third is to claim the high kingship (cores in all Ireland, Ireland recieves cores in Alban if not already present, and starts a war).
During a war for the high kingship, if not totally defeated or victorious; partial victory; recieve Ulster, but lose other cores in Ireland. Partial defeat; lose Strathclyde (if they have it) to Ireland and all cores in Ireland, become a vassal. Larger victory and defeat described below.
2. Alban emerges from a re-Gaelicized Scotland, or 'Emperor of the Gaels'
Ireland lays claim to the Gaelic provinces of Scotland (Ireland recieves cores in Gaelic regions in Scotland). From a Gaelic legal standpoint, these regions must submit to the high king; the people are considered 'Irish' for all intensive purposes, and, since they obey Gaelic law, should submit to the king of Gaels. Ireland can make this claim solely by legal right, or, they may also send gifts and tributes to the clan heads to assure them that they will maintain their legal status and authority when they submit to the king of Ireland, and even be given substantial favor that their Inglis kings would not give.
Scotland's kingdom can deal with Ireland's claim in two ways. Go to war (with a chance of Alban seceding, or the regions joining Ireland, if Ireland has sent gifts; perhaps have two types of gifts Ireland could send, the more expensive of the two would cause the latter, the less expensive the further, and no gifts would keep them from seceding {should be expensive for Ireland to do so, but worth it incase Scotland goes to war}); this would keep them on the 'Inglis' path, or, assert legal claimancy by declaring the king himself to be of Gaelic descent (pay heralds to invent this descent, or have church records poured over for free; the latter would carry a chance of Alban seceding due to insult that such a lie would be forefended in the name of keeping their loyalties {if Ireland has paid off the clan chiefs with the large bribe; the smaller bribe would cause no secession in this case}).
If Scotland declares the king Gaelic, Ireland can demand legitimacy, though it'd cost Ireland money (sending various experts on the matter to test him themselves {Gaels did do things rather like this, but on a smaller scale}). That is, essentially, forcing the king to prove he's a Gael (adopting language and custom). This might convert Lothian to Gaelic if he does so. If he doesn't, again, risk of Alban seceding as the clan chiefs reel from the insult of his lie, and the promises of Irish assistance. Everything up to this point should be a set up for things to spiral progressively further out of control.
Having proved his dedication to his Gaelic ancestry, he may now face a bit of a crisis. Ireland can demand his submission; Ireland will abandon the cores in Gaelic regions, if he submits himself as vassal to the 'Emperor of the Gaels'. If he does so, the kingdom becomes Alban, but part of it should secede into/remain Inglis Scotland and start at war. If it does not submit, a huge blow to relations, but no major fireworks yet.
Scotland can begin a move to further Gaelicize the population (doesn't matter if submitted or not), or let it fall. If they do the further, they lose any other cultures but Gaelic, and become Alban, placation of Inglis lords (costing a fair deal of money) or deal with their secession into the 'new' Scotland or York; Alban recieves a core in Ulster. If they don't continue to Gaelicize, they don't lose other cultures, and remain Scotland, but recieve no cores. They may further try to distance themselves from the series of events with Ireland, as war is growing more likely, if they've not submitted, and actually return to Anglicization (again, possible Alban secession, Scotland goes back to a series of events representing Anglicization of Scotland; Lothian becomes Inglis {again}).
Gaelicization continues; Scotland becomes Alban, loses other cultures. Placation of Inglis lords (costing a fair deal of money) or deal with their secession into the 'new' Scotland or York. Once the war is done, or the lords placated, they can make a legal bid for the high kingship of Ireland. In doing so, both gain cores; Alban gets cores in all Eire, Eire gets cores in Lothian and Strathclyde, as well as the Grampians and the Highlands (which they'd already have), and a war begins. Alban may also, again, choose to submit. In doing so, if they have Northumbria, it becomes Gaelic, and a serious 'York' secession threat ceases (though York may cede itself into a nearby kingdom if able to); Strathclyde become part of Eire, but all cores Eire had in Scotland disappear (though they gain one in Strathclyde if they don't have it already).
If war; war ends in a victory; Alban takes control of the provinces in Ireland, 'annexes' it (becomes the high king), recieving all of Eire's territories. An event for recognition as 'Emperor of the Gaels'. The inverse; Ireland conquers Alban, taking control of all of the provinces it has in Britain, and takes all cores as their own. Alban is submitted to Ireland, either as a vassal, or totally absorbed. Eire's king recieves genuine recognition as 'Emperor of the Gaels'.
In both cases, this can be parlayed into another event. Eire, now genuinely enforcing ancient rights, or Alban, now inheriting those rights by way of their new authority, may make Wales into a core, as parts of it had been settled by Gaels. Obviously, this starts a war, but that's a whole nother series of things, though much briefer and far less complex; essentially, Eire or Alban (the winner, whichever) gets the right to go and take Wales. With it under control, a set of random events determines if it converts to Gaelic culture or revolts (the latter being most common, until Wales does change to Gaelic, in which case these extra large culture revolts cease).
3. Other aspects of a Gaelic kingdom; Gaelicization events, that occur in this order, to Gaelicize regions (all build up for claiming legal right to the high kingship). These would convert provinces to Gaelic culture as far south as Northumbria
Gaels do not have individual land ownership over anything except what land you till/ranch directly, or where buildings you've had erected sit. Thus, no tenancy. Events for Gaelicization would include the revoking of tenancy and land ownership. Would cause revolts in Inglis provinces, but move toward a free population from serfdom.
Gaelic nobility is elected through tanistry. As tanistry is strengthed in Inglis lands, again, revolts may occur, by disenchanted nobles. The move would be from aristocracy to plutocracy. The tanist elected is chosen in large part because he is healthy, intelligent, and has enough wealth to pay his soldiers (since Gaelic soldiers are not tenants and cannot be forced to fight, they're more expensive {free population} than in a feudal or stricter monarchic kingdom).
Movements toward a free market; economically Gaels were largely anarcho-capitalistic, though not totally (they had, by contrast, a few socialized portions of society). That's why individual wealth meant so much for the nobility; they had to be able to effectively maintain a business or some sort to keep up their expenses and allow themselves to maintain their position; a bankrupted noble had to forfeit his position. Taxes could only be raised a set amount, and went into a dole; the treasury was not the nobles' personal bit to use, it was property, technically, of the clan from which it was levied, and could only be used to fund public works (specifically roads, hospitals, militia armories, and asylums; all clan territories required them to be paid for first, and the first dole of taxes went to maintaining them), and was also, to an extent, allowed to be used to pay the army (the problem was, there weren't enough taxes to actually fund an army, so he had to be able to raise an army himself out of pocket). The move would be a little away from mercantilism.
Gaels were, as a mass, very traditional. Would have a nudge toward narrow-minded, though not remarkably so. However, the strengthing of traditional values is very important to the creation of a Gaelic kingdom, since everything is based on precedent and tradition. As such, Alban or a more heavily Gaelic Scotland (that is, a Scotland where Gaels were not marginalized) would also be substantially less likely to convert from Catholicism; Gaelic law, by this point, is as much based on cultural traditions as it is religious, and monastaries still held a good amount of legal power (and churches and monastaries were the only bodies that could own land they weren't developing in some way).
After tradition is encouraged come the final aspects of genuinely adopting Gaelic culture; language, and clothing law. The latter may sound odd to be so serious, but they were very serious about it. Gaels had three types of dress based on social class, with the use of colors and various symbols that represented many things, and held a very high position of esteem. The lower class wore trews/breeches, with a thigh length shirt, the middle wore a knee-length shirt called a leine, with a plaid or checkered shoulder-cloak called a brat, and the aristocracy could dress as such, but also in decorated robes and longer cloaks. These were signs of wealth, power, and respect, and very important. Language, obviously, is a major facet of a culture. Enforcement of Gaelic language should be a big deal. This movement should cause additional revolts, but then, convert certain provinces to the Gaelic culture. This would move another point toward free population and plutocracy. By the end of it, Alban should be about midway between aristocracy and plutocracy, and closer to a free population than serfdom.
Sorry if that's all way complex and confusing, but trying to think of an interesting and realistic way it'd play out, which would not be very simplistic at all.
4. Other considerations; just random ideas and thoughts
Military philosophy; Gaels inherited a pretty lengthy Celtic tradition as fortress builders. The Irish ringforts (cashels) and Scottish brochs were pretty well defended. The Normans found often in Ireland the best solution was to seige, as assaulting the Irish forts was very dangerous due to their unorthodox set up. Coupled with block castles or towers, they were pretty foreboding. As such, one could argue Gaels would be more defensive than offensive. Gaels didn't often fight offensive wars, though historically they had at various times, and done so with great success. I'd give them a bias to defensive but near the middle. Possibly have a specific fortification event for them, instead of the normal one, talking about the establishment of many additional minor forts (which is what they did) pushing them more toward defense, with an antithesis being the desire of the princes to raid more (lowering relations with a few random kingdoms, or even giving some a cassus belli), pushing them toward offensive.
Wars of religion. As mentioned; Gaels were on the whole traditional. Even when accepting new things, they tended to cling, most especially, to religion, when they had any real ability to. Might become counter-reform Catholics, since they'd actually have the clout in this history to do things of that nature.
'The White Martyrs' were Irish martyrs who set themselves adrift on the ocean. Several reached North America, as evidenced by the setting of connemara (green marble, which only comes from Ireland) markers, as far as modern California. Some mention of them in some capacity, when exploring the New World, might be interesting.
The Crusades; even in real history, both Irish and Scots participated in the Crusades, and the Reconquista. Having not been marginalized, some times to Jerusalem, maybe even an event or two, could be in order.
Legend obsession; Ireland's history is largely legendary and they were very serious about it. The Irish believed quite fervently their ancestors came from many regions, but specifically parts of northern Iberia (Galaecia) and around Aquitane. Events giving Eire, or Scotland if they control Ireland, cores in those regions, could provide some excuse for lengthy wars over unusual properties in Europe one might not initially associate Gaels with.
Okay, think I'm done talking for now.