The Breezes resorts are the "family-friendly" arm of the Sandals resort chain. They specialize in activities designed for young children through the teen years. The Sandals resorts are for adults couples only. Both the Antigua and Bahamas (Nassau) resorts have gambling onsite and there is a casino in St. Johns, Antigua. It is a short cab ride from the Antigua resort to the casino but far enough away that walking is not really an option. It is frequented by more locals than tourists - it was when we were there a few years ago - but that may have been because we were there during their carnival in July. Sandals is constantly advertising all sorts of deals to try and increase patrons. (I get e-mails almost daily with free night offers, upgrades in service, etc.).
We have not been to the Bahamian Sandals so I can not comment about their casino.
Sandals Destinations
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Enjoy your trip and good luck at the poker tables!!! 