The kids club is at the sister resort the Tamarijn a short ways down the beach. You can walk or take their golf cart shuttle. We just came back from the Tamarijn and our dd had a blast with the kids club and their staff.
Divi is a great place to stay, but the Tamarijn is a better one for smaller children. The Divi has a much better beach though. See pix of the Divi and Tamarijn at www.geocities.com/THEFEEL2002 It's a free site that shuts down often for an hour as it is overviewed. Keep trying. Also see www.megaresorts.com
We go to the Divi AI every year with our 4 year old. And have a blast every time !! From the pools and the beach and the nightly shows (which my little one LOVED !!) There is never a dull moment. Have fun !!!