Agree - items 1-3 are covered and Pedro's for pizza and video games!
4 - fun activities for kids: snorkel at Shark Ray Alley/Hol Chan; take a golf cart ride south to view birds, wildlife, etc; walk the beach daily; collect hermit crabs; take a golf cart ride north and stop somewhere for lunch and let the kids take a swim in another place's pool; eat breakfast in town on the beach (Estels' or Lili's); visit Amigo's del Mar dock to observe sea creatures; go fishing off a pier; play on playground in Central Park; visit Mar de Tumbo beach on weekends
5 - hotels/condos: Banana Beach, Banyan Bay, Miramar (*Owner disclosure*), maybe the Palms or Royal Palm?
I also have to agree with SJ in that Belize is not Turks, so if you are expecting an all-inclusive, 5 star resort in a hotel zone, this may not be the place for you. However, if you have a sense of adventure and can handle beautiful natural scenery, a variety of snorkeling/diving spots, lots of great places to eat and some of the world's nicest people, then Belize may be a good fit.
PM me if you have more questions. Our kids (ages 3, 6 and 8) are regular visitors and can't wait for their next trip!