The Oceaneer Club/Lab (or at least one) will be in Open House mode the full day until late afternoon. You are welcome to stop by there with the kids. As mentioned, the pools, AquaDuck and water play areas are nearly deserted -- I do believe the nursery takes a "field trip" to Nemo's Reef at some point during the day. Movies are offered, the sport deck is open, the spa is open. Dining is available onboard. There may not be a lot of "programming" offered (i.e., mixology, towel folding, trivia, etc.), but the facilities are all open for those who choose to remain onboard.
Enjoy your cruise!