Can a 16 year old decide when to come for visitation?

You can file a motion for contempt. A custodial parent generally cannot frustrate or undermine visitation, they have to make the child available for visitation. However, there's also the reality that older teens want to spend time away with friends rather than hang out with either parent. If the 16 year old is unwilling to talk to you about visits and work with you on a more appealing schedule, having a contempt motion would at least get the other parent a lecture from a judge about not letting children run the house.