I have always used USPS, and it got to the resort just fine (did this for the Swan, Dolphin, and I forget where else, definitely Hawaii I shipped stuff to a Marriott and a Starwood hotel).
Also, last year I realized my kids needed a few clothing items (the day before we went - they each needed a pair of shorts, sweats, and a sweat jacket), so I ordered from Hanna Andersson and had it shipped overnight. The first day, it was sitting in our room when we got back from Epcot (we were at the Boardwalk resort). I didn't even need to call Bell Services - they left it in the room for me. That was really nice!
The Swan and Dolphin do say the reserve the right to charge a fee, but I never got charged. I send down specific snacks that I know my kids and I like.
Even with a car, it saves time as we can just stop for drinks on the way to the resort. I also hate to wait for luggage!