This past summer we vacationed at an all-inclusive in Jamaica with our 4 kids ages 16, 13, 11, and 9. The name of the resort is Jewel Runaway Bay. We stayed for 5 nights in two connecting "water view" rooms for 3200. (Not including airfare- we used points) It was GREAT!! Your kids are the perfect ages for this resort. There were a TON of kids ages around 8-14, and they all hung around with the "counselors" all day doing organized activities from lazer tag in the morning to capture the flag and Manhunt on the beach at night. If you have kids around this age, they will find friends for sure! The resort also has a small-ish but brand new water park with several slides and a lazy river. Most water sports were also included. The food was great, the drinks were plentiful, and the kids were entertained. What more could you want??
The resort isn't opulent at all, but it's clean and has a great island vibe. There are three pools, two of which always seemed to have lots of activity going on. In fact, my kids are torn between going back here (we were just there!) or back to Disney (where we haven't been in 5 years), if that tells you anything. Good luck!