I dunno, Tywin straight up wanted to drown Tyrion in a river when he was a baby, he might be against kinslaying of all things.
On the other hand, it would be MUCH easier ruling a kingdom when Joffrey isn't around to fuck shit up. Tommen will be much easier to deal with. Unless he ends up banning beets, then the kingdom will probably starve and civil war will kick up again.