I have only done re-lamination by peeling the skin back and drying everything.
There is a video on youtube showing how to inject the glue under the skin. A little simpler for you since it's directly under the fridge vent.
For injecting, I'd suggest liquid polyurethane like Gorilla Glue. If it is still damp the Gorilla Glue reacts faster with moisture. Cures in an hour or so but I'd leave it clamped up for a couple of hours.
You'll need to use a sheet of plywood or particle board as a pressure pad over the de-laminated area as the glue will expand while curing. I've heard several on rv.net say they held the pressure on it by parking close to a building as Kayteg1 said.
I used 2x4s and built a frame around the camper to push against. Then clamped the pressure pad in place using Erwin hand clamps.
Good luck.
P.S. hope you got the leak stopped or it will happen again.
Joe and Evelyn