Welcome to the DIS boards!!! As to your question..no, you are not allowed to use any other pools at WDW resorts....just the pool at your particular resort. The only exceptions to this are the pools at the AllStars..you can use all the pools at the various AllStars..Music, Movies and Sports. Same scenario at PO..you can use the pools at Riverside as well as those at the French Quarter. But, those are the only exceptions.
There is signage at the pools stateing that the pools are 'for the use of guests of the 'xyz' resort only'.