Our 3-year-olds love to swim. So the Diplomat and Disney (Swan/Dolphin) were perfect. Both have outstanding pool facilities, and also kids programs.
Our kids starting going to Disney at age 2. They love it. YMMV.
Not domestic, but it might as well be, you might want to consider the Sheraton Nassau. Great pools, great time of year weather-wise, lots of activities for kids and parents, great value with the downgrade from 4 to 3, so you points go a lot further. Maybe splurge for a suite on points!
Cheers,