Do they have a mobile vet come in on Sundays for rabies shots, like the one in Orangeburg?

Yes they do

The Petsense located on Garner's Ferry in Columbia does have a mobile vet perform various pet shots. Simply call the store management to next mobile veterinary scheduled visit.

The one in Columbia has been Saturdays.

Dont know If its every Sunday. U may wanna call the location and ask. 😃