We also have a 1998 Suntrek. In 2016 I repainted the interior, right over the original wall covering. Last year we did the exterior. We have a great little Sherwin Williams paint
store and they recommended a paint that is used to go over wallpaper. I should have some left at the house, will check tonight on the name. It worked great, trailer looks really nice if I do say so myself. We have the same issue in spots with the edging trim, but not much. I would be tempted to crazy glue it back in place then paint over it rather than try to remove it.