You don’t mention your coach or year.......(might be a water control system valve set wrong on some coaches) but if you log on and do a forum search there have been many posted troubles with shore water filling up fresh water tanks (common issue). I doubt its your hot water heater, it is typically a bad check valve in the coach water pump that has not closed (possibly from some plastic bits stuck in the valve) and it basically allows shore water to go backwards through your fresh water pump into the fresh tank. You can try:
1. Shut off shore water; run the coach water pump several times to try to clear the valve out; then go back to shore water and see if the fresh tank is still filling.
2. You can purchase a stand alone check valve off amazon or local RV store (anti backflow valve) and plumb it into the water pump plumbing line (either side of the pump should work or where it is easist to install into the existing water lines between fresh water tank and pump). This separate valve will prevent shore water backflow or act as insurance for the water pump check valve if you get that one working again.
3. Some water pumps may allow replacement of the built in check valve.
