Jeffz has it right and thanks SandraL for the kind words.
A flexible drain hose similar to this http://www.rvupgradestore.com/index....OD&ProdID=2361
(except without the shown fittings) will go from the sink to a white PVC pipe mounted on the wall. The white PVC pipe will go through the wall and over the furnace; it will have a thermal sleeve to protect it from any furnace heat. The white PVC pipe will connect to the existing black PVC vent pipe next to the furnace; this vent pipe is under the cooktop.
When the sink is down the flexible drain hose forms a P trap. When the sink is up the flexible drain hose is somewhat taut and the sink stopper will keep out odors.
This picture shows blue tape where the wall next to the cooktop is supported by framing. The top tape lines are for the support for the cabinets above the cooktop. The bottom tape lines are for the support for the galley countertop. The vertical tape lines are for a support for the wall.
The white PVC pipe for the flexible drain line and small hot and cold water lines will penetrate the shower wall below the bottom tape lines. The hot and cold water lines will be rigid white trailer plumbing that connects to the water lines under the galley sink; they will have a thermal sleeve to protect them from any furnace heat.
The sink will be mounted to the right of the vertical tapes lines, at about that the same level.
The only part that worries me is increasing the strength of the aft shower wall. Iíll need to cut it open and slide a structural support (plywood or marine plastic sheet perhaps 1/4 to 1/2 inch thick) between the aft shower wall and the original framing. The structural support will attach to the framing supports noted by the blue tape lines. I may add a few bolts to attach the structural support to a wooden spice rack that I may add above the cooktop. Iíll patch the shower wall with a sheet of pre-cured fiberglass sheeting perhaps the approximate size of the entire aft wall so that it would not be obvious.
Itíll probably work; I just donít want to cut open my beloved trailer.