I like to believe (as does a large portion of the fandom) that Robert only had that "love" for Lyanna because she was a female version of Ned. With that in mind (and considering that Jon Arryn was the most important male figure in Ned's life), how would Robert behave himself with a daughter of Jon Arryn?
So yes! This is the return of Jon Arryn's daughter on this blog. I already mentioned that Rhaegar would be obsessed with her, merely motivated by the idea of completing a prophecy.
I think Robert would see her as his first love. And perhaps, his last because she has a tendency to keep him in line.
She, despite having a sense of honor, would not be afraid to expose her claws and a sharp tongue, "So, you got a woman pregnant? You're lucky I won't make you marry her."
However, she forced him to take care of Mya.
"Don't be an cretin, Robert" Her eyes flickered with clear menace. "Go visit the girl and see if her mother will need anything."
(Jon learned that the best thing he could do was let his heiress rule. Otherwise, he himself was the target of severe criticism.)
And with that, we have Rhaegar Targaryen. Heir of the Seven Kingdoms, creating expectations and being miserably frustrated when he realized that the pleasant maiden of his delusions was a rigid and calculating woman.
