Sounds like some confusion on what both are calling different tanks? I think you mean the hot rod is what we see in the picture/ If that is true we more often would call that the water heater tank, not the fresh water tank. Fresh water tank is a big plastic tank the is mostly hidden. the idea is that we CAN add water to the big pastic tank and haul it around for whenw e want water without having a place to hook a hose. The pump has a line from the fresh water tank and it will draw water from it and send it to alll the other parts of the RV, including the ot water tank.
That pump has a system to sense how much pressure is on the water lines and if the pressure is low, maybe near 20PSI, the pump will turn on and build pressure back and shut off, That is whty there is not any problem with running the pump and having the city water connected at the same time. If we have city water, it will almost always be above 20 PSI and the pump never comes on! We normally don't turn the pump on and use battery power if we are hooked up to the city water that already has higher pressure, though!
I left off some parts on that first drawing. this closer to the idea.
You have a big plastic tank and it can be filled different ways. Some have a seperate port where you can stick the hose in and water goes to the tank OR some have a valve that sends it to the tank or direct to the RV and depends on which way the valve is set. Where exactly the connections are madeis not likely to be totally corrrect as I drew them but the idea is that there is a one way check valve built intot he pump that should keep city hose water from going backwards through the pump and overflowing the tank. Water can come in from the hose and go to the RV but not back through the pump to overflow the tank! the one way/check valve stops it goes that way!
But when you are connected to hose/city water, the pressure from that water will be higher than what the pump controls will let the pump come on. The pump comes on, if the switch is on but only as long as the pressure in the line is low. So if city water pressure is there, the pump won't try to come on and pump! The city water pressure is already higher than when the pump will shut off, so it never tries. But we usually leave it off to save battery power until we want water from the tank.
Simple plan is that all the parts of the RV should get water, whne we are hooked to city water or if we turn the pump on and it pulls water out of the big tank and also sends it to the water heater tank. Water gets hot there when something like your hotrod heater is turned on, comes out a differnet pipe to go to all the faucets and shower!
One thing to maybe watch carefully is to not turn the water heater on when the water heater tank is empty! that may let the hotrod get too hot an might burn it out?? Not used one and not sure of that but being careful, until you know!! The way you might find out is when it has burned out!!! UGH?
Maybe this is the correct drawing for what you have or maybe close. It shows two places where you might add water direct from the hose or fill the tank. What's behind the little door???