There is a huge difference between pets that remain living "on board" a cruising vessel and those that are "imported" into a land-living situation in another country.
I have cruised the
Caribbean from
Florida south and east all the way to Trinidad and back several times and never had a problem with "on board" cats even in the islands that are noted to be strict about animals.
Even with dogs, the folks I know who
cruise with them along the same routes only get reminded by the officials to not bring them ashore.
I even got a USDA certificate in
Puerto Rico once, but nobody in any other country cared or asked about it. All they wanted to see, when they did take notice that I had pets on board - was the Rabies documentation from the Vet who administered the shots. Even when the Vet's document was in a different language they only wanted to see "when" the Rabies shot was administered.
However, that being said - you DO NOT want to take an animal into Trinidad - IF you plan on flying back home from there with the animal. A pet on board is not big deal - but if the pet has to transit via an
airport the procedures and costs are extremely expensive.