Thank you for your follow up.
If the father would not consent to your daughter moving in with you or to stop his abusive behavior, then someone in your position would have to document any and all abuse toward your daughter and any of negative remarks about you made by the father to your daughter and then a petition to modify child custody
can be filed with the court which has established original custody and all the facts about father's abusive behavior and daughter's alienation of affection
that are being caused by the father's negative remarks about the mother
can be brought up to the judge's attention and the judge will review evidence and testimony from both sides and will decide whether to modify custody, based on what will be in the best interest of the minor child.
Also, your minor daughter does not decide with which parent she gets to live, since she is 14 years old, she will likely be considered old and mature enough to testify at the court hearing and to state her preferences as to the parent with whom she wants to live.
Also, any type of child abuse or neglect, can be reported to police and child protective services by you and your daughter, to help document and build your case for child custody modification.
I wish you the best of luck!