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[Game of Thrones] Tyrion doesn't do that thing before fleeing King's Landing... How do recent events changes? (Spoilers)

If Tyrion didn't kill Tywin and simply left King's Landing how would Tywin have reacted to recent events such as Jon Snow avenging the Red Wedding and Dany coming to Westeros and the reveal of the White Walkers?
gpt
I think the big change would be that the High Sparrow would have a much harder time getting his claws into the city as a whole and Tommen in particular. The loss of Tywin as a substitute father figure to the King and a moderating influence on Cersei flung open a door for the sparrow that would be otherwise closed; the former no longer needs to find someone new to turn to for guidance, and the latter both A) would have less need to arm the Church Militant with Tywin there to coordinate Lannister military forces and B) have less leeway to make that move on her own, since he'd still hold the title of Hand of the King. 

In essence, half a season worth of television up to and including the **(SPOILER ALERT)** demolition of the Sept of Baelor would be averted, or at least dramatically altered to be much less in Cersei's favor. Expect Tommen to remain on the throne with Margaery by his side, and the Sparrow still doing charity work in Flea Bottom. Cersei would have dodged the bullet of being publically stripped and shamed, as well as the pain of losing her son, but would not become Queen on her own, and be stuck in her same rut of being next to but not in power unless she does something drastic; without the Sparrow to back her into a corner, she might not be willing to pull any triggers as dramatic as the one at the Sept. 

Tywin might be willing to come to terms with Jon and Dany, but it will mostly be with an eye to put them up front on the firing line against the Walkers; not only is this the war they're best equipped to fight, it's also the war that can sap their resources enough to force a proper negotiation after the fact. He knows his history, and knows that conventional Westeros fortifications and armies aren't going to help much against the new Targaryen army, unless he can get them to commit (or lose) their fire-breathing trump card up north. As for the Red Wedding, he didn't give much of a damn about Frey before, he certainly isn't going to start now that A) they've made a massive liability of themselves and B) they're too dead to be of use as a scapegoat anymore. Expect an absolute minimum of fuss to be raised re: the Late Walder.