Hi Mark, this is how I have handled the problem. Sorry but I do not have any pictures. Joist do run the length of the trailer, but joist below wall are supported by metal "out rigger braces" every so often. You just have to cut back to good wood before brace, where you can do a splice.
Whenever I have had to replace bad flooring in a RV trailer, I work from the top down. The membrane on the bottom of the trailer is usually a fiberglass reinforced waterproof material. Once you take up flooring you will probably see several joist that need to be replaced too. On one of my trailers I replaced about 20 SQ feet of floor and joist in the back corner under the tub, and on my neighbors trailer we replaced about 50 SQ feet of floor and joist in the front bedroom due to leaking storage doors. Here is how is was done: On one rain water came in at a damaged refrigerator vent and ran back under the tub in the adjacent bathroom. On the other storage doors for an under bed storage area leaked. You will need to take out any cabinets or items in the area of the damage. I ended up replacing floor joist, and some wall studs too. There are two kinds of wall construction, on some trailers the wall extends past the floor platform which makes removing damaged floor easier. On others the wall sets on the floor plate, and the wood flooring has to be removed from under the wall, then to reinstall you need to jack up roof enough to lift wall so that you can get new floor material under the wall. To remove damaged flooring I used "skill" saw set for about 3/4" deep to get back to good material. To remove damaged joist I used a "triangular shape blade" for my saber saw that lets you cut flush to another surface. If I was working up to a material that could be damaged, I placed a small piece of aluminum sheet below item to cut so as not do damage adjacent surface at end of cut. Also used a "Drummel" rotary tool in some tight places. Used deck screws to install new joist. Predrilled member to attach, so it would pull up tight to exist joist. Used screws to install flooring too. If you need more information send me a PM.
Dr Quick