Hi LsuMom,
Welcome to the Heartland Owners Forum.
The dealer is correct that it's either the 4-way valve or the check valve in the water pump. Fortunately, either one of these is pretty easy to fix.
You'll have to take down the rear wall of the pass through basement storage (near the UDC) to gain access to the water pump and to the back of the 4-way valve.
You should be able to test the 4-way valve while connected to city water by temporarily disconnecting the water line to the fresh tank from the back of the 4-way valve. Use the picture below as a guide. If water comes out of the valve fitting while on CITY, the cartridge in the valve probably has a damaged O-ring. It's a pretty simple replacement and we have some documents and a video that show how.
Here's a link. If this is what's wrong, you can either call Anderson at 800-476-9876, or you can call Heartland Customer Service at 877-262-8032 / 574-262-8030. Have your VIN # ready.
If no water leaks out of the valve, the problem is in the water pump. You can resolve the problem by either replacing the pump, which is also very easy, or by adding a check-valve on the suction side of the pump. The easiest way to install a check valve is to get a $16 Sharkbite Press-On 1/2" check valve.
Here's a link to one on Amazon. You can also find them locally in many hardware stores or a plumbing supply store.
While waiting for parts, turn off the campground water and use your water pump. When you run out of water, switch the 4-way valve to TANK to refill the fresh tank. Then switch back to CITY and turn the faucet off again.