Every time you add more flooring, you can have problems with it being too high and interfering with cabinet doors and other items. Full cork tiles are pretty thick too. Cork laminates have a thin layer of cork on top of something else. Laminates can be pretty thick. Check the thickness and then crawl around on the floor seeing what gets in the way. The threshold at the exterior door may have to be cut also.
This requires planning, but it can be done. Pulling up a glued floor is no fun and probably more work than you want. But make sure the glue is good. You may have to score the floor, try to pull it up and see if the glue holds every where.
If you are gluing the cork, make sure it will stick to the original floor and can withstand temperature extremes. It should be an exterior glue. Check the manufacturer of the cork flooring for advice for installing in a trailer. Observe all recommendations for expansion and contraction. A floating floor will move, but so will a glued one. trim around the edges will hide the expansion spaces.