Solutions for Fixing Interior Plastic Peeling Away?

[ruddneck]

I was away for the entire summer, and unfortunately, the ol' Prizm was left in the driveway to cook in the hot Virginia sun. Consequently, the interior-colored plastic that is next to the (interior) black weather stripping surrounding the car door windows and support posts is peeling up. In some cases it has pulled completely away, exposing the white plastic underneath.

Has any one had this problem before, or are there any suggested fixes? I was thinking about just cutting the the plastic where it had peeled completely off, and gorilla gluing it and the warped pieces back to the door.

Thanks!