No water

If the city water fill valve is turned to fill, the water will not flow from the tanks and water will not flow to the plumbing on city water. Are you turning that valve when you put on the hose to the city water connection? It needs to be set the same when using the tanks and when there is a hose attached for city water.

Does everything work as it should when using water from the tank and the water pump is on?

Is this a new to you Roadtrek?

Roadtrek water use with city water is pretty straight forward. Connect the hose, make sure the city water fill valve is NOT set to fill, and turn on the sink. Air will rush out of the cold faucet and at the same time the hot water tank will fill. It will take a few minutes for six gallons to fill the hot water tank so hot water takes just a little longer to flow. If there was a problem you would see water squirting out somewhere inside or out. There is no filter on the city water line. The only filter is a small filter on the water pump for water from the tanks. I suspect there is no problem and you have the tank fill valve set wrong.

This will not effect your problem but make sure you have a water pressure regulator attached to the hose that is attached to the Roadtrek or the pressure will damage your plumbing.

Check the aerators on the faucets

Sounds like the check valve on the inlet. Look at this for ideas:
valve repair