Any shuttles that pick family's up from the airport to the closest motel to Paris's island and pick them up to take them to base?

I don't remember any shuttle service dedicated to Parris Island. But you shouldn't have any trouble finding one to get you there

I suggest you visit MCRD Parris Island website, it has all the graduation information and contact numbers for further information. You may be able to arrange for a private companyor you may want to consider just getting a rental at the airport.