Okay thank you for the additional information. I can understand why you would feel so upset by the way her step mom is treating her and also that her dad doesn't seem to stick up for his daughter. That must be very difficult to see.
Its always difficult to imagine that he cannot see this and defend his own daughter. But denial is a powerful and wicked defense. Hopefully by your daughter creating a boundary, he will perhaps see how this is affecting her, and make some changes.
For now, what would be best is that your daughter does stay with you and also just take some space from her dad and step mom. She may want to consider limiting all contact with the step mom, or only be in her presence when other people are around, (if even that). If she is emotionally or verbally abusive to your daughter, than your daughter does not need to be around her.
As for her father, she needs to sit down with him and tell him exactly how much this has affected her, and that she would like for him to have a talk with his wife. That is all she can do. She can also tell him that until the wife stops treating her this way and also apologizes to her, that she will not be around her, or coming to the home. That she would like to see him, but only under these conditions, or until things improve.
Counseling would be a good idea for daughter and father, and maybe even some family counseling sessions for the three of them, if they are willing.
It's about setting a boundary and letting her dad know what she will and will not tolerate and sticking to that boundary.
Give it some time and hopefully her father will come around and try to patch things up. In the meantime, it's important that your daughter stay active, have fun with her friends, and interests etc. It's a good thing that she also has you, such a supportive mom to talk with and be with and know that you are committed to her. This is a tough situation, but now that she is older, she can set some boundaries herself. Please click ACCEPT button for this answer. Feel free to continue conversation even after clicking accept. Thank you.