Lots of reasons for low water pressure at campgrounds, versus a city supply. For one, liability. Most private campgrounds will be absolutely certain their supply pressure is comfortably lower than the limits for camping unit water systems. They don't want any issues. Secondly, the supply lines, and the number of units being serviced by an individual supply line, as well as the overall length of the supply line. The hydrants are a variable, too. I used to manufacture water hydrants, such as those commonly found at campgrounds, and variations in the packing gland--combined with age and wear and tear-- influence water pressure.
All that being said, since you don't have an issue when connected to a city supply, it would seem to rule out your camper being the issue.