How do I find family history that orginated overseas?

By your description, you will have the same problem tracing your family history as black people in the US, because the Caribbean and Latin America also had slavery and that's how black people got to those places too. By the way, saying that your father's family is "pure Trinidadian" doesn't make any sense, Trinidad is a very diverse country and there's a lot of race mixing going on there. You already seem to know more about your family history than most black people, but if you want to know more, it's not like you can't just go to Trinidad and the Caymans (and Cuba if you're creative) and do some footwork.