I've had to deal with these types of psychological mind games myself. Because I didn't provide the full and proper itinerary, per my ex-wife's desire, she threatened to prevent me from picking up my children. In that incident, a call to the police was in order. Here's what I learned while dealing with issues like this.
Tentatively agree until you have your kids with you, then "Possession is 9/10's of the Law". Once your child is safe at your place, let your ex know you have no desire to pay and you await him to provide the appropriate tickets. Don't put it in writing, call on the phone. When addressing your desire not to pay, mention your support payments, lack of legal justification to make you pay, etc.
Now the other parent has two choices. 1) Buy the ticket at a premium to see their child. 2) Call the police. If the later, then calmly explain you have no desire to keep your child past the date and time in which they are supposed to return and that as long as the custodial parent provides a means of transportation, you will do nothing to interfere with your child taking that transportation. Ask the police to provide a copy of the court order mandating you provide transportation expenses, and absent one, kindly ask them to tell the custodial parent to provide transportation.
After the ordeal, expect a trip back to court. File first, because you know it'll be coming. Get a motion to Modify that clearly defines who is responsible for travel in your court order. (Research your State Law to know what to expect.)
Probably not the best approach at avoiding confrontation, but it will make sure you see your child and will shift the power back into your hands.
Good luck.
Ian.