I would vote for Turks and Caicos (Amanyara) or Four Seasons Nevis... say Adios to those Avios on American through Miami...
alternatively check out the RC Dorado Beach... also via American...
or maybe Amangani.. AA has good service to JAckson Hole
I am a big fan of keeping it as simple as possible when traveling with babies.. it isn't the easiest thing in the world... we went to Taiwan with a 20 month old and 4 adults and it scarred us for a loooong time...
FDW