quote from an informed friend.
Cersei and Tywin wanted her to marry Rhaegar, but she didn't want Jaime to marry Lysa. She convinced Jaime to be KG so they could be together at KL, but Aerys said no to Tywin about Rhaegar/Cersei getting married. Jaime ended up staying at KL, Cersei ended up leaving for Casterly Rock I think. And then when Elia's parents came to hook her up with Jaime, Tywin offered Tyrion to insult them. So Aerys grabbed Elia for Rhaegar instead to really piss Tywin off. It's crazy soapy style.