I’ve installed “hot water circulating systems” on both my trailers. I did this by teeing into the hot water line at the furtherest sink. I ran a line back to the fresh water tank. Fairly easy because the fill line for the tank was just on the other side of the bath wall under one of the seats.
In the line I installed an inline irrigation valve. They are designed to operate on 24v, but for for short duration they work fine on 12v. Added a door bell button under the edge of the counter at the sink to activate the valve.
Step up to the sink, push the button for 5 to 10 seconds and instant hot water. Water is returned to the tank so zero loss. No need to add an additional pump and an inline valve is less than $15.
I’ve had this on every trailer I owned for the last 22 years (only 2 :)) and it has never failed.