Rebecca:
The refillable mug that comes with the Disney Dining Plan is for use at the Disney resorts and not in the theme parks. So, good news: you don't have to tote your mug to the theme parks.
Interestingly, the mug is in addition to a non-alcoholic beverage provided with each meal on your
Disney Dining Plan. Even though it can be used for refills at the drink station at any resort, when you purchase a counter-service meal at a resort, the Disney Dining Plan also provides you a non-alcoholic beverage
in addition to the mug.
Why would you want another beverage? Milk and juice (orange, apple--think real fruit juice) are not at the refill stations. So even if you're a soda drinker and use your mug, make sure and pick up a bottled beverage either for your meal or to enjoy back at your room or in the park. You've paid for it.
Wishing you a magical vacation!
Whitney