She is afraid of losing her father. She is treating you like this because she is secure in her relationship with you.
She is also old enough to for the courts to take where she wishes to live into serious consideratin. Rather than fighting with her, tell her that you love her and will always be there for her. And let her live with her father if she wants to. She is close enough to 18 that if she decides she doesn't want to live with him anymore and he refuses to let her move back, he won't be able to stop her once she turns 18.
Sometimes you have to let go of your child so that they can learn for themselves what other people are like.
One day, she will realize that her father was wrong to have cheated. And to have put her in the middle of it by introducing her to his gf before he even filed for divorce.