If my husband was married in Trinidad and Tobago, but filed his divorce in NY, is he legally divorced in Trinidad as well as America?

Your question has multiple layers. Place of marriage is, in American law, irrelevant to place of divorce.  Folks married all over the world can divorce in the U.S., and if the divorce is legitimate, MOST places around the world recognize them as such. I have had a couple of cases involving Trinidad, and I believe they generally recognize American legal proceedings. However, you appear to hint that your husband committed fraud in the divorce -- claiming that the wife was served, when she was not, and that he was not a resident of the state when he filed.  If it had been a Nevada divorce, and either of those things was so, the other party could move to set aside the decree of divorce at any time. To be more specific as to the effect in NY, you will have to ask NY lawyer.  Ditto for recognition in Trinidad (you will need to consult an attorney there).