Jim,
I think that your door panel was assembled by spraying an automotive trim adhesive over the molded panel and vacuum bonding the vinyl cover to it. I can not be sure of the best way to repair it without seeing it, but the best way will probable be to spray automotive trim adhesive on the panel where the vinyl has separated and gently reattach the vinyl by using a soft plastic spreader, a heat gun or hair dryer, and your hand or finger tips for the curved areas.
Gerald