The vinyl sections were stretched taut when they were installed. They were probably held on with a combination of adhesive and crimping due to the shape of the panel. As long as the panel was un flexed, the vinyl would stay crimped, and thus stay in place. Unless you opt to take the whole door panel apart, I would try spraying it with a vinyl conditioner like Meguiars #40, Lexol, or some other moist vinyl protectant that moisturizes, in order to be able to stretch it more easily, and then put some adhesive on the inside with a brush, or by masking the area you don't want sprayed, and use a spray adhesive. Then you will need a plastic putty knife, and use it to stuff that vinyl back into the crack, and then you should find something to hold it down with while the adhesive sets. It might not be perfect when you are done-that depends upon the skill of the one fixing it- but it certainly will be better than how it is now, and it will be quicker and easier than taking off the whole panel. Taking off the whole panel MIGHT be an easier way to fix it in the sense of actually getting the vinyl stuffed back in but obviously less easy, because you would need to remove the window cranks and the like. If you want to know for sure what is involved on your particular car, you need to refer to an assembly or shop manual.