Can a Trinidadian file for a divorce in Trinidad although I was married in Texas to a permanent resident there?

I only practicei in Texas. No matter where you got married, you can file for divorce in Texas if you meet the residence requirement. You have to live in the state for 6 months and you file in the county you've lived in for 90 days. You would have to ask a lawyer in Trinidad whether you can file there. It's likely that any jurisdiction has a residency and domicile requirement.