Another vote for wegoshop. Although I've also used gardengrocer, no problems at all, I just prefer the selection at wegoshop. They'll shop at whatever store you want. they get the exact brands and sizes you want. You pay the flat delivery fee, everything else is exactly as on the receipt.
So if, hypothetically, you want them to go to Super Wal-Mart and pick up non-food items, they can do that, as well. Or if your child needs lactose-free milk or you need a pound of kumquats--whatever!
BTW, the DVC resorts have a market area where you could get, say a quart of milk or loaf of bread. It's quite pricey, though. OTOH, wegoshop will do a second delivery for cheap. We hadn't planned to do this, but ended up wanting more fruit and some other items--it was our first DVC trip, we weren't sure what we'd want.