With Tywin still alive, he would’ve seen reason and directed his murderous daughter’s vengeance towards the Tyrells and Littlefinger.
Especially in that Purple Wedding business, in which House Gibbs could’ve stepped in and been the voice of reason.
There was no true motive in Tyrion murdering Joffrey, and while finding the connection between Littlefinger and the Tyrells wouldn’t have been easy, the skilled team would’ve sniffed them out.
The Lannister family might’ve exited that incident much stronger!