[Bill]

If water gets back to the bathroom sink, but doesn't make it to the tub, there isn't much backtracking you can do. I don't know much about your TM's model and year, but lemme ramble a bit.

First, do you have an outside shower? If so, is it right outside the tub? And if it is, do you get hot water there?

Let's start by assuming there is an obstruction as you suggested - a small rock or a clump of something (like sediment as T_C suggested) caught in the valve mechanism. To clear it, you need to get inside the shower's hot water faucet. With the water supply off, do the following. I believe that in the center of the handle, there is a round trim piece. Work a knife blade (not tip) carefully under the edge of the round piece, and it should pop off. Under it you will see a Phillips screw. Remove it, and you can pull off the knob. At this point, you can unscrew and remove the faucet core - the actual valve itself. I don't recall the details, but it should be obvious how to do it.
When it is removed, you are looking straight down the supply pipe. Turn on the water supply JUST A BIT, and water should shoot out all over your shirt - and should carry any obstruction with it.
Assuming you get a gush of water, examine the black rubber faucet washer, and if it is ripped or squashed out of shape, replace it (a ripped washer could actually be the obstruction.) Reverse the disassembly process to reassemble - naturally you kept track of which parts came out in which order when you were taking it apart, right?

If you don't get a good gush of water, then don't reassemble yet. The obstruction must be farther back in the line - perhaps at a right-angle fitting. If you can run a piece of stiff nylon fishing line or grass-trimmer line through the now-open valve body and up the pipe, you might dislodge it. Not too likely, I don't think, but it is easy to try.

If that doesn't work, here is another approach, similar to your compressed-air idea. Reassemble the valve. Then, with the water supply off, turn on the shower valve, and also OPEN ALL FOUR DRAIN VALVES UNDER THE TRAILER. Run a garden hose from your house into the bathroom. Take the shower head off the shower hose, and ram the end of the shower hose into the end of the garden hose. Seal the joint by wrapping your hand tightly around it, and have your wife turn on the garden hose just a bit. This will run water backward through the shower valve, with any luck carrying the obstruction back up through the plumbing and out the drain valves.

Finally, there is one other slim possibility. If I recall correctly (and I may not, it's been a while since I was under there), the plumbing under the tub is done with semi-flexible plastic pipe. If so, it is possible that something pushed on the pipe, and it kinked. Aside from removing the tub, I seem to recall that there are two ways to get access to that area. One is to remove the outside shower enclosure from the outside wall. Remove two screws, cut the caulking, and pull it out of the wall. The second is to remove the wood box-like structure above the head of the tub. Again, remove two screws, cut the caulking, and pull the pieces aside. I have done both, neither is fun, and they provide only limited access - but I bet it is better than removing the tub. Be sure to recaulk when you are done.

Let us know what you find.

Bill