Technically, the language on the mugs say they are only good for the resort you are staying at and for the length of your stay.
However, some have said that CM told them they are good at any resort. JMHO, given your situation, I think that you should be able to use them for your whole stay. It counts as one trip, just a split stay. Once you switch resorts, you will no longer be using them at the 1st resort so its not like you are using them all over. But rather, buying them to use for your resort stay.