If nothing else, sit her down, and let her know you understand her concerns. But also explain the consequences to her. She doesnt stay at dad's and he will file an order of contempt. After a couple of contempt orders it is grounds for change of custody. Which means she would have to live with him and spending EOW with you. It is a possible reality. Happens often. A change of custody would really devastate her from the sound of it. If you think she is old enough to make that decision then she needs to understand the impact. And a side note..... odds are that a Judge won't listen to her wishes. At 12 or 13 they may take into consideration what thier wishes are according to custody. But probably not visitation.
I understand that it is hard for her, but it is important that she stay the night,your freedom could depend on it.