Keith, are there other P traps in the coach that don't get used?
Many coaches have special vent valves on the tank side of traps, because if you dump your tanks (as opposed to leaving them open while camped) to more completely evacuate them, the sudden draw-down creates vacuum in the piping to connected plumbing units. That vacuum will easily suck the traps dry without such trap vents in place. A more recent invention gets rid of P traps, period, by using an in-line valve that prevents odor from moving back through drain piping; manufacturers are starting to use those in coaches, and they likely will become the standard. By eliminating both the P trap and associated vent valve, mfrs. have more leeway when routing drain piping for sinks, showers, and washers. Here's a link to one retailer's description of the HepvO trap:
http://www.a-s-m.com/hepvowastevalve.htmlWe had trouble in our coach with occasional smells out of the shower drain. I finally figured out it was usually after a tank dump, and a couple cups of water in the drain stops the odor. That's the only drain in the coach that I can't find a vent attached to, because the vent is supposed to stand on a short pipe above the trap, and there is no clearance for that under the shower floor. One of these days I may get ambitious enough to install a HepvO trap on that drain; though it might be difficult or impossible to replace the P with a HepvO under the shower, there is pipe access where it runs through the tank bay, and such a valve doesn't need to be near the trap to work.
Just some thoughts for you to consider, Keith. If your coach has trap vents (maybe Gerald or someone knows about what year they began installing them), they are usually a short standpipe with a top fitting that has a slot in it, just downstream of a trap. Perhaps one of them has failed (washer/dryer?) or the slot is plugged or blocked. If so, each time you dump, that trap is being vacuumed dry, because the dump port is much larger than the size of the tank's vent pipe going to the roof.
The "recirculating" vent on your washer... I assume yours doesn't vent moist dryer air to the outside? If you don't regularly use the machine, perhaps it needs a couple of cycles with vinegar, baking soda, or whatever Splendide or the manufacture's instructions recommend to purge it of any odor cause. It is not unknown for mold to develop around seals, even in our home machines. You might consider converting to an external dryer vent configuration if feasible; they are faster and more efficient.
-Joel