If you mean that she betrayed you during the rescue, it's not really a betrayal. She tells you straight up ahead of time (if you talk with her) that she is not willing to get compromised by your rescue attempt, and, if you get caught, she's going to deny that she asked you to save her.
That's not betrayal, that's just her being true to her word. In fact, by ratting her out that she asked you to free her, you are betraying her.
From: IsaacMM | Posted: 2/24/2010 1:56:42 PM | #007 But i still don't get it, didn't she come looking for help because she thought her father had gone mad and was suspicious that he was responsible for Cailan's death? Why would she protect him?
That does not mean she wants him dead.
There are many ways to end his ambitions without killing him.
When you are at Arl Eamon's estate in Denerim, talking to Anora about the whole marrying Alistair Landsmeet stuff, if you so much as mention Loghain needing to die, or needing justice for his crimes, she will turn against you at the Landsmeet. She does not want her father in power but she does not want him dead either.