Probably Tywin joins the rebellion at the gates of King’s Landing. They assault the walls of the city, with 75,000+ men they easily take it. A sack probably ensues without Tywin’s orders, given what usually happens to cities that fight rather than surrender.
However, with Eddard Stark in overall command, it’s quite possible that the murder of Elia and the children doesn’t happen.
What about the wildfire plot? Unless Jaime still kills Aerys & the pyromancers, King’s Landing is going “KABOOM!” before the rebels can get through the walls.
That part would likely happen as in OTL.
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