Thank you for your follow up.
Well, the divorce proceedings would generally have to be initiated where spouses legally reside now, regardless of where the marriage was registered.
So, the divorce would have to be pursued in Turks and Caicos local court.
Here is the link to the island's laws that actually govern divorce process and which you can review:
Also, it would make sense to at least obtain an initial consultation with a local divorce attorney, who can evaluate your entire case and can suggest best strategy and plan of action and also can give you an estimate of what the legal fees might be, should you decide to hire a local attorney to assist you with the divorce process.
Because the island is relatively small, there is not many attorneys who specialize in family law, but you can find couple at the link below:
I wish you the best of luck!