There are a number of places the could work for you:
A. Caribbean Beach resort
1. Nice sized rooms, big resort with a nice walking path
2. Zero entry pools, separate kids pool with a pirate ship, fun for little ones
3. Two water slides at the main pool, quiet pools in each area (8 total)
4. Water sports rentals available
5. Pirate cruise activity (about $30) available for kids 4-12
6. Great variety in the CS so you won't have to leave to eat
7. Playgrounds, sand volleyball, hammocks on site
8. Dedicated buses for the resort, we've found transporation easy there
B. Animal Kingdom Lodge
1. Numerous great restaurants (CS, TS and Signature), room service
2. Animal viewing
3. Kids club on site as well as nightly and daily activities for the kids
4. Zero entry Pool and water slide
5. You might also look into staying on the Villas side, fantastic pool area, children activities at the pool
C. Yacht and Beach Club
1. You've gotten lots of data from other posters, great pool
2. One concern I've read about that area, no real CS options nearby
3. Boardwalk might certainly be entertaining for the family
D. Saratoga Springs
1. Walked through there on the way to DTD, nice place
2. Proximity to DTD could be a huge plus
3. Golf course on site or very close by
4. Good pool areas for kids
5. Big resort so availability is probably good
Good luck with the decision