Don't forget that history is only in the eyes of the historian but it does not really mean that's how it was. I want to address the original question that started all of this:
LydiaTT, They were under Spanish rule as well but what we are now calling Venezuela was a group of provinces (Caracas or Venezuela, Guayana, Cumana, Merida and Margarita along with Trinidad up until 1797) each with its own Governor. The Governor of Caracas or Venezuela was given the title as Captain General and had supervisory authority over the others.
At independence in the 1830s, in the Treaty with Spain, all provinces and islands that belonged to the Captain General's territory were legally recognized as the Republic of Venezuela. The Venezuelans then retroactively apply the label "Venezuela" To all the provinces that formed the CG from 1777 when it was inaugurated.
So from a retroactive Venezuelan perspective the answer is yes.
From a Trinidadian perspective the answer is no as we were a British colony when the Republic of Venezuela was constituted and we weren't party to the Treaty that formed this Republic.
Edited: Cagel on 26th May, 2013 - 7:47am
IndianChick, you are correct. When the Declaration of Independence took place in 1811 to actual independence in the 1830s, all claims on Trinidad would've had to be taken up by Britain. Venezuela recognizes the Treaty of Amiens of 1802 so they wouldn't be ever able to legally claim the island.
Of course, if there would have been a claim on the island by Venezuela if Spain still wanted to contest the British conquest of Trinidad in 1797 as Trinidad under Spanish rule was part of the CG of Caracas and Venezuela demanded that Spain hand over all CG provinces to the Republic of Venezuela upon independence.