We just pulled a UHaul car trailer cross country to get our son's Ford Ranger out to his job in Yosemite.
At most campgrounds, we were able to fit the trailer and motorhome in a big pull through site. In some campgrounds, we used the trailer as our 'parking spot' and just pulled the Ranger off when we needed it and drove it back on the trailer when we came back. In Malibu, we parked the truck in a separate area and they charged us $15 per night since the truck was not at our site.
The car trailer is much heavier so you can't move it around by hand (at least not U-Haul's trailer). It's not like a tow dolly that you can stash by your picnic table, etc.
Tom and Katharine
'07 Winnebago Tour 40TD, 400hp Cummins
RVing for 19 years & 150,000+ miles