Say that Aerys II dies during the Defiance of Duskendale in 277 AC, either because Barristan’s rescue failed or Denys Darklyn killed him outright after Tywin put the town under siege. Does Tywin try to marry Rhaegar to Cersei right away? If not, to whom is he betrothed (I’d suspect some urgency to the matter)? Are Rhaella and Rhaegar wary enough of Tywin’s (potentially) deliberate botching of the affair that they bring in Steffon as Hand? Is there still the potential for a Southron alliance?

Oh, absolutely Tywin marries Rhaegar to Cersei. In fact, if Rhaegar doesn’t, I think he suddenly cuts his head off while shaving, Cersei is betrothed to Viserys, and All Hail Regent and Lord Protector Hand of the King Tywin Lannister. 

And at that point, I think the Southron Alliance changes targets to deal with the Kingslayer Tyrant (in either scenario, really, although the propaganda works better if Rhaegar had died), and picks up the Tyrells to boot, because I think with that much power the crab-bucket nature of feudal politics really begin to kick in.