Here's an idea, but what about romance?
Maybe she fell in love with a member of the court of Solitude, or a supporter of the Empire? (any marryable people in Solitude or Markarth that are part of the Legion, or those that side with the Empire in general as a citizen of Skyrim, or both?). Maybe the adopted childrens parents were killed by Stormcloaks during a raid, and she wants to ensure her "children" or any other children feel that pain again?
As illogical as it sounds, the path of romance, love and the bond between a guardian and child (blood related or not) can be so strong that the "logical" choice no longer applies because the logic has changed. Love can do that to a person.
I would get more in depth but since it is not my story, I would love to see the author fill in the biggest gaps.
Could you keep me posted in a PM how this turns out if you don't do so publically?
Now I expect you to do a "Son of Tullius who joins the Stormcloaks" character.
Numerius, love child of General Tullius and Legate Rikke.
Then Why is she thinking of siding with the Legion? There is no reason to do the Civil War unless you hate one side or the other.
If she loves her father, then she should not side with the people that let the Thalmor, which she despises with a passion, into her homeland, which means she should hate the Empire.
IF she likes the Empire, then she should fight to keep the Empire together, and thus hate her father for trying to break it apart.
Either way, there is hate.
Simple, She has more love for the Land of Skyrim then she has for her father.
No matter which side you agree with, which Side Ideals you believe in, you have to admit, both the Empire and Skyrim are stronger under Imperial Rule.
If the Stormcloaks win, The Legion is dealt a Severe blow to its total military strength, and the Forces of Skyrim alone would not be substantial enough to defend themselves if another war with the Thalmor broke out. so both the Legion and Stormcloaks will be at a disadvantage if a war does break out.
If the Legion is Victorious, it will have assets from Skyrim that will give it more of a fighting Chance if a war with the Thalmor does break out again.
Both the Empire and Skyrim are stronger together, then they are apart.
You character would know this, and thus would fight against her Father for the good of the land!
even then, she hates what he did, and thus hates him.
Then she should avoid the war, if she loves everyone.