Garland and Alerie will no doubt be in King's Landing for the coronation- Alestair might be a bit more at home, and he will probably know quite a few people in the capital. Garland won't want to stay, however- he has a lot more business in the Reach, being in the middle of sorting out half of it's revolts. Alestair on the other hand is a veteran diplomat, and will probably carry their voice if say, a council occurred. 

The Tyrells are going to have a lot of explaining to do about you know, being a neutral force in the whole conflict, but Alestair and Garland know that they're a pretty essential part of running the kingdom. Should be interesting to see what happens...