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Unfortunately, unless either you and/or your wife are residents of the Dominican Republic, you wouldn't be able to get a divorce that would be recognized in the United States.
You and/or your spouse would need to be a resident of the Dominican Republic for a period of six months before applying for the divorce, which is the residency requirement imposed by Florida law to obtain a divorce. § 61.021, Fla. Stat. (1999). Florida courts have determined that lack of residency in the Dominican Republic equates with a lack of subject-matter jurisdiction. See, e.g., Orbe v. Orbe, 651 So.2d 1295 (Fla. 5th DCA 1995). Accordingly, even if your divorce would be apparently valid in the Dominican Republic, which has no residency requirements and which has, since 1971, recognized divorces for non-resident foreigners based on “mutual consent,” Florida refuses to recognize such a divorce. Also see Lopes v Lopes 852 So 2d 402 (5th DCA, 2003).
The point here is that you can get a piece of paper that says you're divorced, but according to Florida you'd still be married. If you tried to marry someone else, etc... that would be a void ab initio marriage that could be annulled at any point after that marriage (because you'd still be married under Florida law).
I know this is probably not what you wanted to hear, but it is the law. I hope that clears things up anyway. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (good or better). Thank you, ***** ***** luck to you!