They have a custody agreement/order (as evidenced by his recording and mentioning the judge). She cant arbitrarily refuse to transfer custody based on looking in the car. And if she does she will have to deal with those consequences. Woman can be petty, spiteful, and overly protective. Her actions were probably a result of all those things. As a man, its best to facilitate a smooth transfer of custody and not engage in petty bullshit... especially if you a parttime parent who just drove 2 hours to see the child. Why further delay that to argue about her touching your car and wanting to secure the child?
This is mindnumbingly imbecilic and immature behavior on his part. If she wants to secure the child in the vehicle and make sure he has a properly functioning car seat then let her and be on your way man. You're a fucking weekend dad.. Make the tranfer as smooth as possible and appreciate the fact she has the kid probably 90% of the time and is overly protective. Recording that dumb shit while refusing to let her do so is clown shit and can only end badly for him.
He looks and sounds like a fucking fool bro.
If they both go in front of a judge for new custody order and they are asked legal basis for both their refusals... She will simply say "i wanted to make sure he had properly secured and installed car seat.". He can only say "I didnt want her to touch my car your honor". Foh.