I've had this happen to three of my trailers. It very common where it gets extremely cold. I bet we'll see a bunch of these posts in the Spring. Use a razor knife and cut around all the cabinets and walls. Remove the sheet and use it for a cutting template. Lay the new sheet loose on the floor. No glue. You'll have a hard time finding a glue that will handle the extreme temps anyway. It needs to be loose laid with nothing attaching it around the perimeter. Self stick or glue down tiles won't work. They will let go when it gets real cold. Just finish it around the edges with a 1/4 round or base shoe molding. Done! The loose lay floor will "float" with nothing holding it in place and will have enough give to not crack. I used a laminate in my last one that did this with great results..
B.O.