Can anyone give a good reason why she would fight against her father.
please do not derail the thread into a pointless debate or I will just request for it to get locked.
Speaking as a daughter myself, I can say there are plenty of reasons why a daughter might take a different philosophical or ideological position than her father. In fact, I would almost say it's likely she might do so.
They may have had a testy relationship. He may have had no time for her. Joining the oppositiion might be her way of asserting her independence. Or indirectly letting her father know he wasn't such a wonderful parent. Or it might be just a bid for attention.
Or she may have been recruited by someone on the Imperial side because "turning" the daughter of Ulfric Stromcloak himself would be a valuable public relations asset. In this scenario you could roleplay that she joins the Imperials to declare her independence from her father and later decides her father was right after all and switches sides. I can see that being an interesting roleplay.
Well, if you want a story about her doing something that gets Ulfric so mad that she punishes her, I have something in mind. But I don't really know what Ulfric's opinions are on specific subjects so it probably wouldn't make sense anyway.
Could also go with a story like she is the illegitimate daughter of Ulfric, and sent a letter to him to take her in as his daughter, but he refused, so she cut all ties to him and fights to get power in Windhelm.
In this case, Maybe she learned things about the Thalmor or learned things that led her think her father's cause for freedom is started at the wrong time or something?
Does Ulfric even know he has a kid, or was she conceived in a trist in Cyrodiil before Ulfric went back to Skyrim, leaving her mother to raise her alone in a devastated nation after a war? Does that, combined with Ulfric's other actions, such as leaving the Greybeards to fight in the war, or leaving her mother to retake Markarth, or killing Torygg to become High King himself, make her view her father as a man who flees from his current duties, obligations, and responsibilities, in order to pursue greater personal glory? Did his abandoning her at Helgen leave a bitter taste in her mouth, especially if she was saved by Hadvar instead of Ralof? Does Ulfric just want to use her (especially if she's Dragonborn,) as a tool to win the war, or does he actually care for her? Define the relationship, and it becomes easier to come up with motivations.
EDIT: Apparently, this was posted while I was writing my piece, which largely negates my questions. You're on your own now.
She had a secret childhood crush on a Thalmor boy who liked her too. When they became teenagers, he spurned her because she was an inferior race. Hell hath no fury like a woman scorned....
Ideological differences have split families apart before and in some cases it has caused them to be on the opposite side of the battlefield. During battle, the only thing that matters is what side you're on until there is a clearcut victor and defeated.
I actually like the idea of the daughter of Ulfric siding with the Empire, only in the end could she not kill her own father. Good story.
Hmm.. so as you say, Her and Ulfric have a good relationship prior to her going travelling throughout Tamriel.
Now, what if prior to Finna going travelling, Ulfric wants her to marry one of his lieutenants to help solidify succession (he isn't getting any younger, after all). Finna, being a strong and independent Nord woman doesn't jive with that notion and this spurs her to go and see what Tamriel has to offer. Now, this doesn't necessarily have to cause a rift between the two, certainly Ulfric can respect his daughter's decision but it leaves him in a bit of a bind.
With his daughter doing Talos knows what at Talos knows where, Ulfric faces increasing pressure to solidify the succession in another manner, to which he eventually caves. Maybe he knocks up one of the local women and has a son, or maybe he names one of his lieutenants as his successor. Up to you which route you go in that regard.
Finna returns to Skyrim eventually and finds out that she has basically been screwed out of her [perceived] birthright. As mentioned, this is something that Ulfric had to do out of necessity, not out of spite. The process can't be reversed though without causing division within the Stormcloak ranks, a fracture that could spell the end of the rebellion and Ulfric's demise; he can't afford it. Marriage offer is put on the table again, but Finna is still a strong and independent Nord woman, she doesn't want to want to play house wife to some milkdrinker.
Experiencing life outside of Skyrim has left her somewhat more cultured than when she first departed, with a new found appreciation of Imperial-related stuff. Why join the legion then? A way, a real way, to get her birthright. You can throw in the whole believing the Empire needs to be united to defeat the Thalmor view-point to make the decision more palatable as well.
Certainly plenty of cases in Europe where families fought one another for the claims to their titles. The Carolingian civil war that led to the http://en.wikipedia.org/wiki/Treaty_of_Verdun is a pretty good example of this.
Too much? Ahh my friend, that was but a sketch in word form. A general overview, if you will. I can craft a much more long winded post, if required.