I've been poking around on this topic in recent days and have come to the conclusion that a recirculating shower with hot water is a very doable solution. Main trick is you'd have to have a semi-dedicated space inside, with a shower pan that isn't rigged to drain to gray water.
It largely comes down to having a small holding tank, a small water heater, a pump, and some filtering gear. Just a matter of putting them all together in the correct order.
Most of the solutions I've found in videos involve being able to draw water out of the fresh tank, and also push the water out of the shower pan into the gray water tank and then pump it back into the holding tank; frankly that just seems like unnecessary added complexity. I'm going to plan on a completely closed system. Drain the holding tank to gray tank manually, drain gray tank at an appropriate location, and fill the holding tank with fresh water at the same time the fresh tank gets filled. Makes your fresh tank go a lot longer.
The guts of the system can be most anywhere in the vehicle, and just run hoses to where your shower head/mixer is, and then back from the pan. Filters clean out any schmutz. If you go with an electric-only heater, put it on a switch and flip it on a little bit before your shower.
One issue with this sort of setup I've yet to puzzle out 100% is when you want to flush this system out (if it even really needs flushing). It's not necessarily a simple task to drain one of those water heaters - seems like it takes pulling it out of its normal space, taking it outside, and flipping it upside down. Not a herculean problem, of course, just a matter of making sure the unit is installed in an easily-accessable spot and can be mounted/unmounted, hose connections connected/disconnected, with ease.
