I believe you said you had a "thankless" water heater. We have one in our rig as well and had the same problem. What happens is that when the hot is on and you try to adjust the cold to cool it down, the heater probably senses the drop in water pressure and turns off. You raise the temp on the wall and try again and the same thing happens but this time you get scolded when you try to cut the cold and the heater turns on again. Completely thankless situation
So what we do is set the temperature to 112F and just turn on the hot water, no cold. We find the water is at a good temp between 110 and 112 for a shower. When we are done, we put it back to the default 115/120 for everything else.
Wile parked and attached to the water supply, I keep my fresh tank full and turn on the pump. It just improves the pressure in all the fixtures. I turn off the pump when it does not cycle on and off while on city which means there is plenty of pressure in the bib.
Hope this helps.