Wow that's pretty rough. I'd call it a rebuild rather than a repair. I'm no construction expert but I think you'll probably have to rip all that rotten wood out and start over. Personally I'd look into using plywood and rebar to hold a form and pour concrete in behind it to make new walls/floor for the pool. I've no idea what that will cost but you might keep it in your price range if you did absolutely everything yourself. I'd search for DIY pool construction.

Maybe someone else here will have better information for you, unfortunately I don't.