To the OP:
You seem a little mystified by the treatment you've gotten here so I will explain it to you. But first, I want to answer your question about how to avoid further complications:
I wouldn't worry about it happening again with this girl, she has very likely moved on to an easier target by now.
In the future you should avoid having silly disagreements with people in foreign countries because you are vulnerable as a foreigner, they know the lay of the land and have many years experience getting over on people like you.
Dominicans seem nice and friendly to tourists but if you manage to wound their pride or sense of self worth they will not be able to rest until they have made every effort to get even, and, as a foreigner you are an acceptable target. I think this may hold true with other cultures as well, but this is the one I am most experienced with.
Now as far as the not so warm reception and lack of compassion here:
This is not really an anonymous website for most of us, most of the regular posters here know each other or have at least met a few times.
Also, you appear to be a sex tourist, to most of us who live here full-time sex tourists are a nuisance at best and many of us have much stronger feelings for the breed. (not good feelings)
Finally, regarding the advice you've gotten about any possible redress, forget it. What you don't seem to get is that here, everyone really is out to get you, the hookers, the police, the lawyers and anyone else you meet. As a tourist of any sort you are their bread and butter.
So a chica tried to extort you. Then the police did. Obviously the chica has police connections. In tourist towns, all of them do. The police would never allow them to ply their trade if they weren't part of the program. You want to complain to another police officer? Who is more likely to be friends with the second police officer? You? Or the first police officer?
Regardless of whether they decide to play good cop or bad cop with you the end result is that you pay money. Which is all you were really trying to avoid in the first place. The amount may vary but it wont be much of an improvement and may likely go the other way.
Lets say you contact a lawyer. He will undoubtedly need money. Then he will drag his feet until you leave town and go home and then do nothing at all while continuing to beg more fees of of you.
So really the best strategy for you is to forget about the hookers you've ****ed off and then stop ****ing hookers off.