A U-Haul dolly is light enough to move around by hand, by people strong enough to move it around by hand. Many consumer dollies are constructed lighter to make this easier (increasing the population that can move them), and some fold for storage.
U-Haul dolly will need wiring for lighting, and a 2" ball at the right height. U-Haul shop will make sure things are set up right, but not all outlets may let you tow their dolly with something other than their truck, they have some rules to manage their risks. They are usually OK with their dolly on a properly wired motorhome.
Your Sonic should dolly tow, if it has enough clearance to fit on that big U-Haul dolly. If your car doesn't fit their dolly (or otherwise is not dolly towable according to their book) U-Haul will want to rent you a trailer, which is unlikely that they will let you tow with your motorhome. Their trailers can also be moved around by hand, by persons strong enough to move them around.