If I remember correctly, 'chichi' is used when talking about your father. If she said 'otousan' it would be refering to someone else's father. (but one would call their father otousan when talking to him).
So if she was talking to someone else about her father, she would use chichi, not otousan. But still, its a bit weird for her to even use that, you think she'd call him the emperor or something.