The vinyl on top of the arm-rest has pulled away from the backing on all four doors so it no longer lays flat on the arm-rest. This has caused the section of the door panel above the arm-rest to pop off (on all four doors). What's the best way to fix this?

I'm thinking of cutting a slit in the vinyl behind the panel so I can get some glue onto the armrest and door, then somehow holding the vinyl in place until the glue sets. After that dries I would glue the panel back on which would cover the slit. Has anyone had this probelm? -Rich