Richard,
Assuming that you have cleaned the screens at all facets, the highest probability of the thing that is causing the most restriction in water flow when on city water is the factory installed water pressure regulator or it's inlet screen. The 3/8 inch hose that you are using is also part of the problem if the campground water pressure is not excessively high. You will get a higher flow rate with at least a 1/2 hose, and a 3/4 inch hose is even better.
The first thing to do is to remove and clean the inlet screen at the city inlet regulator. If that does not give you enough flow, you will need to replace the inlet water pressure regulator. If you replace the inlet water pressure regulator, you have two options. First, if you install another water pressure regulator here, you should use the 65 PSI Shurflo unit. However, replacing the inlet regulator with a non-regulated inlet that only has a check valve will give you a higher flow rate. If you replace the factory water pressure regulator with a check valve only inlet, you will need to always use a pressure regulator at the facet where you hook up your hose.
The water pressure regulator regulator that you choose is important if flow rate is a concern. You should never use a Valterra regulator or one of similar design because it restricts flow. Only use a full flow adjustable regulator like a Watts regulator that is rated at 4 GPM (gallons per minute) or greater. Adjust the regulator to between 50 PSI and 65 PSI. The 50 PSI setting is easier on your hose, but the 65 PSI setting will give you a higher flow rate.
If you want to increase the water flow when on the water pump, you will need to replace the water pump with a variable speed higher flow rate like Aquajet RV series pump that produces 5.2 GPM at pressures up to 65 PSI.
Gerald