The Reach is most likely going to join with The Iron Throne though. You are forgetting the marriage pact between the two houses. The Tyrells may hate Cersei with a passion, but Margaery is still married to Tommen. The Reach will no doubt come to the aid of King's Landing since they have a vested interest in keeping Tommen on the Throne.
The Reach has several problems that should be considered:
1. Ironborn already occupy the Shield Islands. Those islands are right at the mouth of the river leading up to Highgarden. Cersei refused to supply the Tyrrells troops to clear them off the islands.
2. Dorne has it's armies massed along the Reach/Dorne border.
3. Jon Connington and "Aegon Targaryen" and the Golden Company are also uncomfortably close by in the Stormlands. If Dorne chooses to assist them, all bets are off. The Golden Company is 10,000 troops strong. That's not a small force.
The rumors about Tommen's and Myrcella's true parentage is some serious baggage or the crowd in King's Landing wouldn't be calling Cersei "brotherf.....r" during that riot in KL and the Lannister hold on the Iron Throne isn't particularly stable. Especially since Kevan was murdered by Varys' children. And Kevan had been making progress in mending the Lannister/Tyrrell fracture in wake of the Faith Militant's seizing Margaery at Cersei's instigation which is no secret whatsoever to Olenna and the rest of her family. With Kevan gone, it's back to Cersei's misrule since she's the only one left to guide Tommen.
I'd bet Olenna is already figuring out if she should cut bait and abandon Tommen and throw in her lot with someone else once she can get Mace (ha), Margaery and Loras out of King's Landing. She has to realize that if Tommen dies without issue, her family' AND the Reach is up shit creek sans paddle. Particularly if "Aegon" proves he is indeed Aegon to Arianna Martell.
And finally per Maggy the Frog's prophecy, I'd imagine Tommen is going to die very soon. "Three gold crowns, three gold shrouds" remember ? That also may mean Myrcella is going to rule AFTER Tommen because if Tommen dies, she's the last remaining "Baratheon" heir to the throne and she's in Dorne's hands. It doesn't matter if she's female because she'd be absolutely the last known "heir" outside of Dany who can be crowned. Dorne's call whether to marry Arianne to "Aegon" or go through with the Myrcella-Trystane marriage or not.
Prince Doran is a excellent player of the game of thrones to boot. And he has two directions he can go towards. Aegon or Myrcella and has great casus belli in either case.
And I suspect Dorne is massing those armies for exactly THAT reason.
And uh, you remember some of the Sand Snakes are headed to King's Landing ? I'd suspect Tommen is due for a little poisoning with Tyene headed to King's Landing.