With out knowing what primer you have i will make a suggestion. I would look into a waterborn primer as a barrier coat. When a catalyzed primer such as a 2k comes in contact with dried out old enamel it is very likely to wrinkle and when that happens you will end up redoing any bodywork in that area as well as feather edging alot of wrinkled up primer. If you want to experiment on your old doors try sanding thru the paint and apply one very light coat of primer (just enough to achieve light coverage) and let it dry then scuff that and prime normally over top. By doing this you will limit the amount of solvent that can attack the old paint. You may be able to skate by using this method.