I think it's a little of both.
Anora was manipulating things to her advantage. Both Loghain and Anora kind of misrepresent each other. While I feel Anora was exaggerating her danger (from Loghain) if Howe thought he could get away with it, he would have killed her. Possibly even turned it to his advantage by claiming the Warden himself did it. Loghain's motives were partially to protect his daughter, so I don't believe he would have killed her. Did Anora feel that was a possibility? I do believe she may have perceived that. Her father was getting further and further away from her and he does say "There is nothing I would not do for my homeland". I can see her thinking, what would have stopped Uberpatriot from killing his own daughter if it meant Ferelden's welfare? He sacrificed Cailan already, and that was his best friend's child, a man he helped raise like a son. Remember, WE can see what happens at Ostagar, Anora can't. She has only conflicting reports and the ultimate result to go by which left her a widow and clinging desperately to the throne, and an increasingly unstable father who refuses to provide any kind of answers. And there is Howe, grabbing as many pieces of the pie as he can get his greedy paws on, influencing her father, making him even more someone she doesn't know.
So, did she believe Loghain would kill her? I think, to some extent she did, even if Loghain himself admits she was never in any danger from him. We are dealing with perceptions here. No one in the game has a guide book telling them "This and that is so..." and in this respect I think the writing was very well done.
By the same token, Loghain states (in referenced conversation) that Anora would do anything, 'throw anyone under a bus' to keep her throne. Yet, if you say "Loghain must die" or insist in any way he must be punished, she draws the line and sides with her father. Regardless of what she wants (the throne), she wants to save her father as well. She argues logically for his life, and if she loses the argument, accepts what's happened. She's not one to cry over spilled milk.