The retainers create a new clan or go to the civil war. These are vanilla features.
Yoritomo is the heir of the Minamoto clan. He is the special one in this period. If you look at the history of this era, you will notice that he expanded very quickly into Kanto region. However, I also think other clans could have some tools to fight against him. I will consider what I can do for that.
Considering no clan in the vicinity has any chance to withstand Yoritomo's retainer army, I'd say if the relations with a neighbor drop, the player as Yoritomo should be forced to give gifts which delay his ability to buy honor (which pays for his invasions). It's important that clans like Satake and Takeda are actually up for the fight but it looks like at least in the Kanto region all clans are somehow not aggressive at all. Clan Kazusa is sleepy as well. The more Yoritomo grows, the more he should pay to avoid the minors to start plotting against him. That's the how to, in my opinion.
We have honor that prevents new wars, money that buys honor but we need the AI to react to the rise to power of the majors. What's true for Minamoto must be true for Fujiwara and Taira as well since they are playable.
Thinking about the snowball event, I was wondering if you could possibly devise events that increase attrition and defense values when it's winter. That should basically fix the problem of the game having no seasonal changes.
Considering there's no province development limiter is it possible to have the historical regions having REAL castles and developments while all the others (while still being possibly upgraded to the max) having different much minor values?
What I mean is, if Edo is obviously upgradable to a def value of 100 could Suruga have as max def value 50? In other words, do provinces have separate base values and separate upgrade values? This would bypass our limiter problem.
If you also play the Rise of Samurai scenario in S2, I guess you can learn the period quickly.
I have.
I have even played at that point in time, Cinemaware's Lords of the Rising Sun. Specifically designed for the Minamoto.

It was a lifetime ago but unfortunately I didn't learn anything with the history. I know it's a great period but I have no historical reference whereas I have 2 books on SJ period.