Can they move our driveway porta potty for a day while we pour concrete?

Yes, a rental company can move your portable toilet for the day, but you must request it in advance. Most companies charge a separate delivery fee for each move, even if it is temporary, because it requires a truck and driver to make a special trip. They usually cannot combine the relocation with your next scheduled service visit unless the timing happens to align exactly.

Call your rental company now to schedule the move. Tell them exactly where the unit should be placed temporarily, like the side-yard gravel you mentioned, and confirm that spot has level ground and truck access. Also ask them to note the temporary location on the service ticket so the driver does not skip a pump-out. Your current setup, with four workers plus your family, meets the OSHA 1926.51 minimum for a construction crew of up to 20 people, so you are fine on that count. Just be sure the unit is back in place before the concrete crew leaves, or you will face another move fee.

Kim is right about the fee, but I would add that the driver will check the temporary placement for overhead clearance. For a side yard, that means looking for low-hanging tree branches or wires the truck or the unit might hit during the lift. Also, confirm with the rental company that the temporary site is not part of a public right-of-way, which would require a permit. Your driver will not search for a moved unit; you must get the new location on the work order to avoid a missed service.