While they have been a fic or two about Ranma being Pinkie Pie, they are too depressing. So here is my more out beat version!
Ranma used to have dreams about being a pony. He no longer talks about it anymore, cause is unmanly, and is been years since he remembers having one of those dreams anyway. So when one day Ranma finds himself dreaming about being the Pink pony while he is "awake", he has no clue what to do.
Meanwhile, Nerima might not be ready to face a crazy Ranma with pink hair who can apparently warp reality, and wants to be everyone friend.
Turns out Ranma been living two lives, human while awake, a Pink Pony named Pinkie Pie while he was asleep, but not the order has been reversed, and both Ranma and Pinkie remember their "crazy" dreams.
******
Yeah, that's it, no the Pinkie Pie and Ranma personalities do not share traumas, Pinkie Pie and Ranma have their own fears and traumas to deal with. So Pinkie Pie is not afraid of cats, and Ranma doesn't get depressed as easily as Pinkie Pie does. That's because while they share memories, those memories are like remembered dreams to them, so they don't have the same impact. Plus Ranma did not find the life in a rockfarm so bad, while Pinkie Pie, unlike Ranma, had always somepony to calm her after her "nightmares". And by the time both are teens/young adults, they learned to deal with their dreams.
I think that Ranma main problem both in manga and anime, besides being a jerk, is that he sees some things as a kid, not as a teen or young adult, his understanding of love and friendship tends to be a tad naive and child like. He desperately clings to Ukyo because he needs a friend, and his needs of friendship is so much that he was willing to considerer Mousse and Ryoga friends, when those two wanted to kill him. Granted at least Ryoga had been his friend in the past, and protected Ranma when he ewas weak as a baby, but he has no excuse about Mousse.
He also tends to forgive things easily, like a kid does.
I also thing that the reason he wanted so desperately for Shampoo to love him back, was not his ego, but the fact he is a broken bird and desperately craves affection.
Sure, this mostly counts as AU and alternate character interpretation, but it fits somewhat with his actions. If Ranma did not crave affection so bad, some of his actions would not make sense.
And Pinkie PIe, she desperately wants EVERYPONY to be her friend.
Well, dunno if I can make this work or not. I will try to write a few pages as soon as inspiration hits me.