Yes, mug is good for split stays. This last time we purchased at SSR, then after a few days went to WL. Mugs worked seamlessly at both.
Curiously, it seems that for those with split stays and dining plan, they issue mugs at resort #1, and a new set of mugs at resort #2. As we were walking around hotel on check-in day, a very kind couple, seemingly with a large bag of new mugs, gave us a couple, explaining that they did the split stay with their family, that both hotels issued each family member mugs, that as a result, they had way too many mugs, and that they were leaving that day and needed to offload some of them.