Glitter Bay Apartments in Barbados.
The resort comprises of apartment blocks all in an old hotel style resort. There are a variety of apartments to choose from. This obviously gives the opportunity to self cater, get take aways or dine out (I'd never recommend AI in Barbados as there are so many gorgeous restaurants). There's a lovely pool & a kids pool (& a small kids play area) & it's on one of the best beaches in Barbados (we saw turtles laying eggs last year). Both my DS also live the Concorde experience & watching the planes at the airport 
. There are so many other lovely trips too.
There's a bar/restaurant on site. It's only open until sunset & can close sooner if the occupancy is low, but the food is lovely (small menu with daily specials). There's also the Fairmont Royal Pavillion hotel next door (you can eat there) & a beach bar called JuJus a short stroll down the beach, with the Lonestsar restaurant (lovely) just past that.
There's a concierge there so they could arrange babysitting & as a lot of the apartments have their own housekeepers, they will (for a charge), often make you a meal. It's also really secure. Some apartments have housekeepers who will so your washing & ironing (we came back with none to do 
)
You're a short bus ride into Holetown & there are various 'wildlife' type tours to do (see the green monkeys, turtle trips, submarine trip etc). It's really easy to drive around the island but not essential. You could hire a car for part of the hol to get around & then bus/taxi for the rest.
I've also stayed at other places in Barbados, but Glitter Bay is the only place I'd go to again.
I've travelled to St. Lucia & Antigua (pre kids) & Barbados 4 times (with kids). I loved St. Lucia but feel it's not an easy island to get around, especially with kids. I didn't much like Antigua at all, but that's personal preference!
The weather in Barbados, St.. Lucia, Antigua etc will all be much of a muchness, so pick an island & go from there
Any questions, just shout up. I love Bim