The only thing that I can think of is to have baby monitor and take chairs outside the room onto the walkway and use it sort of like a balcony/patio area. Bring a good book, some knitting, electronic games, etc and set up for a relaxing wait. Mid day, if you have a stroller that reclines flat, perhaps the little one can nap in there while you walk around world showcase or sit in a shady/hopefully quiet area by the lake?
Some luxury resorts (such as the Grand Floridian or Yacht Club) have common lobby areas that can be quiet where a little one could have a nap while you people watch/relax in a secluded seating area. Again, you would need a stroller that allows napping, though.
You can get in room babysitting in order to get some adult evening time to yourselves. My son and DIL used this when they went with our 2 year old grand daughter in June last year and it worked well for them.