You just made the situation 100x worse with this.
Unfortunately for you, the situation you set up for yourself is pretty much going to be decided for you, and this depends on who Ulfric likes.
Even if the girl has "daddy issues", Ulfric's not in a position to just his daughter go like that, unless he wrote her off and disowned her.
Let's say you do this: no man would go near the girl unless she's out of Skyrim. The civil war alone puts risk on the relationship, and should the couple be captured, don't pretend daddy won't favor his little girl even if he disowned her. He'll just take it out on the man dumb enough to marry her.
If things are warm and fuzzy, the man will literally fear the ruling relationship and if the girl does run to him because he's acting like a True Nord, you can bet Ulfric will put down the spanking.
It's lose-lose unless your girl packs up and gets her butt into Elsweyr or Valenwood ASAP. Black Marsh may be suitable as well, provided it's hospitable to Nords. Point is: get as far from dad as possible if girly wants a happy family.