What should you do when a 16 year old girl is refusing to comply with a Michigan child custody order?

It sounds like you would benefit from consulting with a custody lawyer in Japan.

Its Complex -- and generally its a waste of money to do much except to try to get the child to agree -- which may be impossible. So Dad.. get ready to fly to Japan periodically to see your kid for a while (she will not likely come back before she is 18 years old and an adult not subject to the US court's parenting plans by which you could keep her here until she is an adult). Be nice, kind, respectful and love your daughter. At least attempt to talk to her often. Do not be aggressive, do not threaten, coerce, do not be passive-aggressive, etc. I am dealing with a similar situation where a child in Italy does not want to come back to the US for the father's parenting time. Its being litigated simultaneously in a US court and the Italian Court. The kid (and mom) have been in Italy for 5+ years and have dual citizenship. They were allowed to move to Italy by the US Court. Now that the kid is grown up she does not want to come back (she has reasons that are essentially immaterial to this discussion). The Italian Court using Italian law and an international child rights treaty seems to be upholding the Child's right to decide. The dad, an Italian national, is spending lots of $$ pursuing his rights in the US court. The US Court is disregarding the Child's wishes, the Italian Court's order and even disregarding Italian Law and claiming jurisdiction. The US Court is entering orders that punish the mom for not complying with the US court order to send the child back -- when under Italian law she cannot force the kid to get on an airplane to come to the US. The Italian Court will probably not enforce the US Court's orders ... So stalemate.. and lots of wasted $$. It is a complete a MESS or SNAFU (using military jargon). But the upshot is Mom will probably not come back to the US anytime soon (and may soon be subject to a US Court warrant for her arrest), the Dad may be subject to the Italian Court orders if he goes back (because the US court has cut child support and the Italian Court will most likely re-institute it so he will be subject to arrest for non-payment of support) and the child is very fearful if she comes back to the US she will be stuck since the dad is trying to change custody and she is afraid to be stuck here in the US! The dad is spending thousands (if not tens of thousands) on attorneys and will probably never get any relief..