The water pump is not in play when on city water. Other than it may have a bad check valve letting water flow into the fresh water tank.
You should check the screens at each faucet. If you don't have a screen on the shower faucet it should flow freely.
You could have a bad pressure relief or regulator.
Is there any sign of water running out of the bottom of the coach?
Is there a screen on the city water inlet?
Do you have normal flow when using the pump? If so I would expect the pressure regulator or pressure relief.
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