We could go full-on AU: Rhaegar deposes the Mad King after the Tourney at Harrenhal, Elia dies giving birth to their third, Lyanna marries Robert, and Rhaegar never re-marries until growing unrest in the North means he needs to take a Northern bride and Sansa comes to court.
Or if you'd rather a father-son gen line instead of shipping, we could have Rhaegar survive the Battle of the Trident, be hiding in Essos all this time, and eventually come seek out his son. Which could also lead to Rhaegar/Sansa, actually, now that I think about it.
I could make us a custom if you'd like to discuss further!