I had to cut out and remove a lot of soggy wood from a fiberglass TC. The floor was made like a boat on this one and just held water.
Yes, first find all the leaks and repair them, not to factory standards, but to a non-leaking standard. Go over-board and be paranoid like your life depends on it as you are about to do some major repair work that you will not want to ever do again.
Expect a major renno!
Do it right, put proper drains in the floor so when water does get it it can get out fast, but no so that water can get in through the drains.
Does the repair have to be wood or can you use another material that is waterproof?
Do remove all damaged wood as black mold is something that can happen. Get it all out.
There is MOLD BLOCK spray and other mold removers you can find at HD or hardware stores to deal with any mold. Remove all mold so it does not come back, it will get damp or humid behind the walls.
Good luck, I do not envy you.