We stayed at the DLH last November, in the Bonita tower and we had a small refridgerator and a coffe maker. Was not expecting either, so it was a nice surprise. You could always ask for a room with one. As for a store that sells milk on the premises, I can't tell you. HTH.
There's a place near the Neverland Pool whose name is escaping me now. They have packaged deli lunches, breakfast pastries, etc. And, I believe you can purchase sodas, milk, etc. there, too.
We were there only 1 night, but a truly magical experience. Yes, we also had a small fridge
in our room. We went to the store by the pool and purchased milk, bowls of cereal and danish for
the kids to have the next morning.