From the looks of your pictures, it looks like the leaks have been happening for some time due to discoloration. My guess is that the OSB board it not water proof, and it has swelled up, as can be seen for what looks like "gaps" in the edge of the board. Board has swelled leaving a rough surface and caused the under liner to tear up.
My main concern would be to find and stop leaks before preceding with repair. I would say that floor board panel should be replaced with a waterproof board and a new under liner. Also I would recommend that edge of new floor board be weather protected with some sort of Alum flashing. Also if leaks originate higher up, there could be wall damage too.
I have seen a Video on how to replace the floor in a slide, and it was quite a project, as it required bracing slide to the ground, so that wood floor panel could be replaced.
I have done leak repairs on three trailers and in all cases once I started, I always had more damage to fix that was seen on the surface. Had to replace wall paneling and even studs and floor joist. Even an entire roof.
