I did get the idea that a "split stay" at a different resort on the same vacation it would be permissable to use the same mug. But I wasn't sure what type of "rules" apply if the mug is obtained through the dining plan, especially like in my case dining wasn't purchased through the entire split stay.
Since all the Resort Quick Service locations sell the exact same mug designs I think to myself why would anyone who does a split stay want to purchase the same mugs twice on one vacation? So I say once you buy the mugs at your 1st resort then you can use them at the 2nd resort you stay at.