The Renly-Tyrell plot absolutely hinges on Cersei being executed and her children being outed as bastards/probably killed too. That clears the way for Margaery to become queen without previous heirs in her way. But where is Tywin in all of this? He wouldn’t take the execution of his children lying down, and honestly he probably wouldn’t believe the accusations anyway. What do you think he’d do, and what would the outcome be?

Tywin might well rebel, but he’d be fighting the Stormlands, the Crownlands, the Reach, the North, and the Riverlands, with his only options for allies being the Greyjoys (who burnt his fleet at anchor) and the Martells (who want him dead). That’s not a fight Tywin can win.  

Also, it’s not entirely necessary that Cersei and her kids be executed – Robert would certainly want that, but Renly might suggest instead that they (and Jaime) be held as hostages.