You didn't say where you are based, or the age of your child. Both can have significant influence on your choice of destination.
If you are in NYC or IAH your choices may be different. With only four days, you will want to minimize travel time and airport-hotel transit time which can be a problem in UVF (St. Lucia). Many St Lucia hotels are 1 - 1.5 hrs from UVF which is located in the SE corner of the island.
On CUR, consider the Marriott.
BGI -- the Hilton. Barbados is rarely bothered by hurricanes.
MBJ -- the all-inclusive Hilton is only 15 mins from the airport and it has a FREE kids club. (Was free three years ago.) MBJ also means a shorter flight from the US mainland.
--
13F