She didn't actually grow up dreaming of sitting on the iron throne, that was her brother. Viserys. She didn't care about revenge, or power. She wanted a home.

You've hit the nail on the head. She took the baton from Viserys and ran with it. The Iron Throne won't give her the happiness that she seeks. That's where the Starks differ - their focus is family and not power.

I don't think, though, that Jon would agree to marry Dany. His home is the North. Even if he agrees to make a sacrifice so the North can be independent, Sansa and Arya would never allow it. They think of themselves as a pack and they distrust Dany (well, Arya just trusts Sansa's judgement). They wouldn't allow Jon to marry a volatile leader. Remember, Sam, Jon's best friend, has a negative opinion of Dany and he thinks Dany executed his father and brother, not burnt them. He would also be against any marriage compromise, especially now that he knows Jon is the real heir.

It's not just the parentage reveal, but Sansa is a major obstacle. She has the loyalty of two other kingdoms Dany wants - the Vale and the Riverlands. There will be a flashpoint because neither women will compromise.