Joseph,
On my 2015 2551 (just a short version of the 2552) it came with a 4-way valve at the city water inlet (on the driver's side). Is that what's on your city water inlet? Or is it just a single hose connection with no valve selector?
Back when they used just the single hose connector and no selector, the city water inlet connected to a cold water line at some point AFTER the water pump. Thus, the check valve in the pump would block water from the city hookup flowing backwards into the fresh water storage tank and over filling it.
Typically, if the fresh water tank over filled, the vent hose in the fresh water tank would vent water (instead of air) to the gravity fill section on the passenger side and you'd get water dripping (or flowing) down the passenger side on the fiberglass.
If that overflow line had a leak, or bad connection to the fresh water tank, the leak could also, or only, be inside on the right rear (as viewed from inside the coach) of the water tank.
With "dismally low pressure" as mentioned by Volkemon, that check valve may not be seated properly and could allow some water to backflow, fill the tank and leak out the vent hose.
If that's not what's happening, then it sounds like you have a leak in the water line from the pump back into the bathroom toilet, sink and shower.
And that won't be easy to find or repair.