You get refills at your disney resort, TS meals, and if you buy or have a plan where you get the refillable mugs at your resort. At the parks, CS meals you do not get a refill unless you fill your own drink at that establishment.
We carry around a resort mug in a bag and get refills when we stop at resorts for dinner or a visit.
You can buy refillable mugs at Typhoon Lagoon & Blizzard Beach. If you buy a mug at one of the water parks you can later buy a sticker for another day at a different water park that is a little less expensive than buying another mug.
I hope this helps and any other information anyone else adds
If you are talking about TS restaurants, then yes you get refills on your drinks. At CS establishments, you do not but the large drinks are quite large and we've never needed a refill. If you have purchased the mug at your resort, you are free to fill it from the drink dispensers - I do not believe milk is included and my kids don't drink juice so I wouldn't know about that.
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