What am *I* supposed to do in regards to my ex's 'parenting time'?

Ask your lawyer for proper guidance on how to handle a person who refuses to abide by a court order (make sure he is properly served at his current address with regard to the supervised visitation). As for the supervised visitation, have your lawyer ask the court that this be done on a visitation center. Whatever else you do, do not let him see the child unsupervised as that is against the court order and if you do, you could lose custody of your child to Social Services as you may have endangered your child. If necessary, let him go back to court with his allegations of you refusing to let him see the child and the court can explain his limitations and restrictions to him. Take care.