Hi Heather, Welcome to Flyertalk.
AA doesn't consider the Caribbean to be International for purposes of lounge access. So unfortunately, no, you won't have access based on your itinerary.
You can buy day passes to the AAdmirals Club, but if you have Centurion already, I'd just stick with that. AA lounges, other than Flagship First/Business, aren't special enough to warrant spending $ to get in, IMO.