Hello Marilyn!
Purchasing a Disney Souvenir rapid refill mug at my
Walt Disney World Resort for use on my Walt Disney World vacation is one of my favorite things! Typically, once you purchase this rapid refill mug at your Walt Disney World Resort and have it activated at the time of purchase, it is usually good for refills for two weeks (14 days), according to my experience. Also, you can refill them at any Walt Disney World Resort as long as you are within the time period of use after activation. Keep in mind that these mugs are not refillable in theme parks or water parks, but only at the Walt Disney World Resorts.
So for your split stay at two different Walt Disney World Resorts, you would only have to purchase the rapid refill mug at your first Resort, and it should be good for your second Resort as long as it is still with the 14 days from the first purchase.
I like to keep my refillable mugs as souvenirs of my Walt Disney World trips, and when I use them at my home, they remind me of my Walt Disney World vacations and the great memories that I made.
I hope that your next Walt Disney World vacation is truly incredible in every way!
Marc L