A little update.
I chased a few ideas around for having a hot water option for my 6 x 12. Nothing permanently mounted appealed to me. So I bought a 4 gallon Stainless Sprayer tank and "plug it in" to the trailer
when I want to. I sewed up an "Insulated Cover" that does an amazing job keeping the water warm for hours on end. Maybe something like this would fill someone else's needs.

I put the connections in the rear corner of the trailer. This area is actually under my awning and awning enclosure so it is near a power plug for quick heating and also a good spot for a private shower. And, 4 gallons gives a better shower than say 2 gallons which my wife tends to appreciate.
This whole method gives me an awful lot of options. In the trailer, I do have a dedicated hot pump and solenoid that allows me to circulate water to the tap and then back to the tank rather than waste any cooler water in the tubes. The pump with solenoid engaged allows me to send water not just back to the tank, but also via a 3 way valve on the tank, to an exterior shower head or outdoor faucet depending on which is installed via the Push to Connect fittings.
Of course the tank also allows complete independent use via the original hand pump (or compressed air cylinder) without the trailers electric pump.
Heating the water also has a lot of options. If I have 120v access or my generator along, I drop in an immersion heater and it heats 4 gallons to 110 degrees in about 15 minutes. If I am camping off grid, I can also pull off the bottom half of the insulating cover, and put it on any propane or butane stove. Or, I can even drop the tank into a hot bed of coals.
I also have started experimenting with a DIY 22" x 22" solar water heater that uses as many wraps of 3/8" tubing I could fit into the area sandwiched between black ABS plastic and a clear top. In testing, circulating water with a small pump through my solar experiment also keeps the water over 100 degrees quite easily. At some point, I will permanently mount this solar water panel on the roof, and it will only have water in it when I'm hooked up... Unless I find it effective enough to use on site just from my cold tank for washing dishes or hands. I'm really looking forward to finding out.
Lastly, I once made the "boy scout water heater" system with a copper coil heated by charcoal feeding a 5 gallon bucket. I'm thinking of building something similar to see how many briquets and time it would take to heat 4 gallons.