I do not practice in WY, but I may offer some general advice. If WY is anything like WI (and I suspect it is), the child may never refuse visitation while s/he is a minor. It is generally the parent's responsibility to make sure the child adheres to the visitation schedule. If the parent does not enforce the visitation schedule, the other parent may contact the police to enforce the schedule or file for contempt sanctions against the offending parent. Contempt sanctions range from fines to jail.
When the child is 18, a legal adult, then s/he may refuse to visit a parent.
Confirm this advice with a local, experienced family law attorney.
This will depend on where the visitation order was issued, because that State's law will control the situation. If you have a Wyoming order, then there is no particular age at which a child can refuse visitation. However, for all practical purposes, once a child reaches about 15 to 16 years of age, the Court is not going to "force" the child to visit. On the other hand, the custodial parent must always make the child available for visitation; a custodial parent cannot deny visitation to the other parent just because the child does not want the visit. This is especially true in cases of young children. For example, if a child is less than fourteen years old, but does not want to go to Florida for a visit, the non-custodial parent should probably put the kid on a plane anyway.