I am replacing my Door Panels and rear Side Panels, corners and edges are curled and loose. But the Trim pieces are all good. It looks as if the trim was laminated to the Vinyl at the factory. What would be a good strong glue to glue these on? Would headliner glue work?
Try this before you give up on your original panels. Go to the auto parts store and spend $20 on a vinyl repair kit. Using a heat gun (or your wife's blow dryer) heat up the damaged areas and the vinyl will soften and become very workable. Stretch the vinyl back around the corners, glue it, and clamp it. Let the glue dry. Heat any cracked vinyl, shove a little glue under the crack, weight/press it down and let the glue dry. Then go back and fill cracks using the vinyl repair kit.
I did this to my trashed door panels and they look almost perfect now. I even messed up a few areas and simply cut out my mistakes and refilled with the repair kit stuff until I got it right. Very rewarding in the end. It was kinda like body work. I just kept at it until it was right. I suppose you could take them to an interior shop and have them worked also.