Water damage is terrible and chasing a leak can be worse. Winter is on the way and finding that leak should be first or tarp it. I wouldn't put too much money into repairs until that leak is found.
Leaks can come from all kinds of places, wood tends to wick and will draw water. Without being there and ruling out all inside possibilities: water lines, joints, hot water heater, pump, even an over pressurized FWT can wick water up, sink drains........ and all of these items might only leak under some situations(pressurized, unpressurized, running…). Water can and will travel many many feet before it shows its self. Start by drying everything up use a fan and/or small heater. Now lets get it wet again, If you are sure it is coming from outside use a small sprinkler head and start small, build dams and or tape off window frames to reduce area being watched. (Quick Thought,You said it was in a pop-out could there be a lawn sprikler out side spaying up) Use a flashlight inside, touch things and be patient. Sprinkle for an hour and watch, then let sit an hour and watch. If you found it narrow the area if not expand. Once you find the leak find the best way to seal based on where its at, many products are best used in different situations. Finding leaks can be really tough and even if you have a "professional tech." do the work, check the work with a sprinkler head(dont let him/her leave).
My parents had a leak near a slide-out and had it "fixed" 8-10 times, over 4 years, before they sat in the driveway of the shop and used a sprinkler to check the work. There is no other way to tell if its fixed until it rains which could be months depending on time of year.
As for fixing the damage you need to do what’s right for you. From your post sounds like you don’t move this trailer if this is true you might just fix the bench. Again not being there and knowing the situation makes it tough. Campers do come apart and can be fixed/patched up either to original specs. or what ever is needed to make you happy.