Dale, I've done many, (too many) repairs like this on plywood in sea-going yachts. If this were my trailer, this is what I would do:
1. Establish the full extent of the damage by stripping back plastic veneers, insulation, carpet, etc. Bear in mind that damage inside the board can travel a long way. Try to get 6 inches of apparently dry board round the damage exposed to the air.
2. Dry the area very thoroughly. This could take days. I sometimes put a 60 watt light bulb in an inspection lamp cage close to the area which needs drying.
3. Brush away any material that is so damaged as to be easily detached from the surface.
4. Use a sharp probe, like the point of a throwing dart, to establish the full extent of the softening. Then decide whether or not to do the major dismantling of the walls which is necessary for a replacement of the damaged panels. I can only guess at the damage from your photo, but as the damage is not cosmetically important, I would probably not do any dismantling.
5. Having decided against dismantling, I would obtain a supply of penetrating epoxy from, for example, www.rotdoctor.com
6. Drill or spike a series of 1/8 inch holes all over the damaged area at 1/2 inch intervals. The holes should not go right through the material, but stop just short of the other face.
7. Soak the damaged area with the penetrating epoxy according to the pack instructions. Repeat until the holes are all filled, and no more epoxy soaks in. Allow to set.
8. Bring the damaged area up to full thickness by making a filler with normal epoxy and colloidal filler powder (I use WEST products. www.westsystem.com
). Allow to set, then sand smooth.
9. If the area is structural and non-cosmetic, I then epoxy bond and screw a piece of 1/2 inch marine ply over the entire damaged area. I then epoxy coat this cover plate, before painting to match the surrounding area.