Refillable mug questions are touchy subjects here. The answer is No, you cannot use a mug at another resort unless it is one of the "sister" resorts, like the All-Stars and POR-POFQ.
I read on these boards that YES, when switching resorts, you can use the refillable mugs purchased at the first resort, at the second resort.
It is quite often this subject comes up! Hold onto your receipt when you purchase them.
Refillable mugs are good only for the length of your stay at the resort you purchase them at, except in the case of sister resorts, like All Stars, or POR/POFQ, or YC/BC, etc.
I bought mugs from WL (stayed for 2 nights) and then switched to Poly for 1 night and bought mugs from POly. It is a great souvinier!!
I would feel unconfortable using WL at Poly. The way I see it (in my case) that if I can afford to stay at Disney, I should be able to afford to buy us the refillable mugs even if it means buying more because of the split stay.
You might try asking a CM if you have your receipt. But the usual practice requires a new mug at each resort. It isn't Disney's fault that you are staying at several resorts.