In most states, a child that age can pretty much call the shots. Ex's financial obligations, however, do not change. If he is not doing what he is supposed to be doing per the judgment, then you can bring a contempt action to enforce his obligations.
Regarding your daughter, the first question is if she stops going, will he make an issue of it? Now, he might try to bring a contempt against you claiming you are interfering with visitation. Contempt is only found if there is a knowing and wilful violation of a court order, and here your defense would be that it is not you interfering, it is daughter's wish. If you want to head off the possibility of him filing a contempt, then you file a modification seeking to terminate visits with daughter. If you do find yourself in court on this, either by his contempt or your modification or both, it is very possible that an interview with your daughter by a third party gauardian ad litem will be ordered to determine her views (she will never appear in court). If she has legitimate issues and this is not just some exercise of teenage wilfulness, her views should carry the day, but possibly with the stipulation that she and father seek counseling together to work thru their issues. Court or no court, effort should be made by both to repair their relationship.
To questioners from West Virginia & New York: Although I am licensed to practice in your state, I practice on a day-to-day basis in Massachusetts. I answer questions in your state in areas of the law in which I practice, and in which I feel comfortable trying to offer you assistance based on my knowledge of specific statutes in your state and/or general principles applicable in all states. It is always best, however, to work with attorneys and court personnel in your own area to deal with specific problems and factual situations.