Other Issues: Automobile Insurance
You have two issues. The first is whether or not the Court Orders state how any additional costs are to be split between the two of you. Do your Court Orders include these types of costs?
The second issue pertains to the insurance coverage. Does your son have his own car? If he has his own car, it doesn’t matter who actually obtains the car insurance. The issue will be whether or not you both agree to split the expense.
Will he be driving your or your ex-wife's vehicles? This is a trickier question, and one you need to address with the insurance company. Since auto insurance follows the car, if he is going to drive any of the cars at either of your two households, you each will probably have to obtain insurance for him. Since he essentially splits his time equally between you and your ex-wife, he will be deemed to be living in each of your households. As such, he would be considered more than a "permissive user" (occasional driver to whom you give permission to drive your car, and who is automatically covered under your auto policy.) Since he lives in each of your households, you will need to add him as a named insured on each of your policies.