Can you purchase auto insurance for your son on a car owned by your ex-wife She would hold the title to the car but you would be listed as the responsible party?

Generally speaking the owner of the car insures the car and lists the people who drive the car as operators. This is regardless of whether the primary operator lives in the household or not. Some insurance companies will allow the person who has care custody and controll of the vehicle to insure it whether they hold title or not.