Spoilers - Don't read if you have not seen season 6 episode 5 of Game of Thrones.
In S06E05 of Game of Thrones, we see Sansa and Littlefinger meeting. Here Sansa is shown super-kickass and talks to Littlefinger. However, she is fully aware of the war to come at Winterfell. Given the circumstances it is obvious to hate Littlefinger and not trust him. But having an army of Vale soldiers behind her would be good in the war at Winterfell. Yet she dismisses Littlefinger and vows never to see him again.
Is her hate for Littlefinger more than the chance of getting Winterfell back? Or is she just being short sighted about the prospect of having Vale soldiers behind her?
Littlefinger has already proven that he cannot be trusted and that he is only on his own side, definitely not on Sansa's. While he may be - right here and right now - offering her the army of the Vale, she is smart enough to know that at a moment's notice, he could change his mind and turn that army on her. She knows that will absolutely happen if Littlefinger decided betraying her would be to his advantage. Then she and Jon would be fighting a war on three fronts (WhiteWalkers, Boltons, Littlefinger/Vale). In her opinion, taking on just the two fronts without Littlefinger's army is a significantly better option than risking the very likely possibility of having to fight a war against both them and the Vale soldiers who were commanded to betray her.
I think Sansa is playing the Game of Thrones. She realizes that she cannot trust Littlefinger to have her best interests at heart, and as long as he is involved, he has some power in the North, which she does not want.
She believes that she is better off taking the North under her own power than allowing Littlefinger to continue to have control over her.