Anne,
Thanks for asking your question to planDisney!
The
Walt Disney World Dolphin Hotel and the
Walt Disney World Swan Hotel share a refillable mug program that is similar, but separate from the Disney resort hotels. You can use them at both hotels, but no, you cannot use them at a Disney resort hotel, or in a Disney theme park.
As for your question about the refillable mug in the parks, there is no such program at this time. Disney resort hotel guests who use the refillable mug program in their own resort hotel cannot use them in the parks either.
Regardless of where you stay, the refillable mug programs are usually a great deal for many travelers. This is especially true if you are going to be spending any time at the pool. The savings start ringing up rather quickly. There is also a mug program at Aulani, Disney's resort in Hawaii.
BONUS TIP
The Swan and Dolphin have numerous refill locations where you can replenish your drink. At last check you could refill them at
Picabu,
The Fountain, and a number of other locations. Check when you arrive to get a full list.
Have a Magical Vacation!Doug