Wish list: beachfront on a gorgeous beach (think Grace Bay or 7-Mile), calm waters, safe, accommodat

Wish list: beachfront on a gorgeous beach (think Grace Bay or 7-Mile), calm waters, safe, accommodations renting a car with a full kitchen, pool, a few kid-friendly activities around the island, "easy" to get to (okay with taking a ferry).
Honestly you aren't going to find an abundance of "organized activities" for children ages 2 4 on any island - you are going to be their main source of activities and fun no matter where you go. That said, most islands have resorts restaurants that will be "family friendly".
If you liked Grace Bay and 7 Mile Beach you'll probably like Anguilla. Topographically, Anguilla is similar to Provo Grand Cayman but it's much more laid back and quiet. renting a car The beaches are fantastic and for the most part are lapped by calm clear waters - perfect for families renting a car with little children. Look at Shoal Bay Villas.
Have you considered Aruba? No vendors they are not allowed. Divi resorts has kids programs renting a car but since I am a senior I do not know much about them, but there is a room I see where kids do activities associated with Divi. I am sure most of the hotels offer this in Aruba. Nice beach, safe island, and the Divi Phoenix has a great beach for little ones.
We took our 18 month and 3 yr old to Turks and Caicos, and it was perfect. Ocean Club West has the condo accomodations you are probably looking for...amenities but not the craziness and high prices of Beaches.
The following year (kids ages 2 and 4), we went to Anguilla and stayed at Shoal Bay Villas renting a car in Anguilla. This was in 2007 so not sure if they have been updated...not the fanciest of accomodations but what they lacked in style was made up for with the location...RIGHT ON THE BEACH! Though not as long as Grace Bay, it's just as beautiful. Great dining options on Anguilla and it's just a very cool, laid back place. I highly recommend Junior Fleming who has a glass bottomed boat - awesome trip for the little ones...he even tried to teach my littles how to snorkel!!!