With Dominican citizenship (can I assume good Spanish?) you might have a chance. Here's what's transpired in that segment of the industry...
Eight to ten years ago when the brands started to pass along their pattern making to Dominican contractors (and reduce their in-house patternmakers) the market was very good for a qualified patternmaker willing to move or commute to DR. No one on the island was skilled and few from abroad yet felt the need to look to other countries for employement. At that time the ability to earn a 6 figure US$ salary as a first rate patternmaker in DR existed.
However, since that time, most of the larger manufacturers trained in-house Dominican patternmakers & CAD/CAM employees. These locals are now skilled at patternmaking from a basic measurement chart, draping, doing fittings, communicating with designers, etc. The capability to grade and make efficient markers also exists. For the most part, these people work hard to keep their jobs as it's their best shot at a semi-decent (peso) wage. You'll find that Accumark is more commonly found than Lectra's softare.
With the decline of the industry overall and the better trained Dominicans, I'm afraid you'll have a bit of a challenge finding a job. I suspect the larger companies all have their staffs in place now, but in Santiago you could contact Interamericana, D'Classe, & Grupo-M as a start. Should be able to find contact information on the web. The little guys may not be able to afford you even if they need your skills.