My child has stated repeatedly that she does not want visitation with the non-custodial parent. Does she have this right?
No, a child doesn't have the right not to visit.
The reason for this is that it isn't her decision to make- the court has ruled that visitation shall take place. The only person that can legally refuse visitation is the non-custodial parent.
You should not be letting your child get involved in this; it's improper to allow a minor child to make these kinds of decisions.