Hi Holly and welcome to the Disney Parks Moms Panel.
In short, yes, you can!
Once purchased, guests with refillable mugs are able to enjoy refills at any Resort self-service beverage location for the entire length of their Resort stay.
So, for example, if you will be staying at
Disney's Yacht Club Resort and purchasing your refillable mug there, once purchased, you can use it at any of the self-service beverage locations at any of the other Disney Resort hotels for absolutely free.
The easiest way to find the self-service beverage locations at each of the Disney Resort hotels is by heading towards the Quick-Service dining locations.
Wishing you a magical trip filled with memories which will last a lifetime!
Emma