Most if not all stores will allow mobility scooters into the stores and some stores including Walmart have their own mobility scooters for people who need them.
I've seen several people drive their own mobility scooters into the stores and drive them around the stores as well.
Store aisles are usually designed to accommodate most mobility scooter sizes however larger mobility scooters may not fit through the aisles.
Most stores will not forbid your mobility scooter because that would really be discrimination against the disabled so if you really need the mobility scooter you will almost always be allowed to drive your mobility scooter into the store.