No doubt your camper has now been through a few winters. Our last camper shower / tub surround was installed in screws. Second or third year we owned it, we had a very harsh winter. The extreme cold caused the plastic surround to shrink slightly. Well, screws have no "give" at all, and something had to "give." It did, the surround cracked. We never replaced the surround. I just puttied the crack and pumped liquid nails behind the cracked area to help seal it. Fortunate, it was near the top, so water behind the surround was not a serious problem.
My suggestion, Liquid Nails, no screws for the same reason. Liquid Nails does have some flexibility to it, even after it dries completely, which will also expand and contract witsh the heat and cold of the seasons. You don't need to use a lot, just the edges, and you'll be good.