Not all Dominican mothers are robots and consider children as objects of sale. This autoresponse is old, boring, not true, and bitter.
Saying that it will not be difficult. Dominican woman can and are like women all over the world, wonderful loving mothers and would not be separated from their child for all the cash in the world. Full custody will not happen, but you can work over the next few years on visiting several times a year and proving yourself, continuing to be a good provider as a father should, eventually you could very well end up in a good situation where she will allow you to have the child on extended visits to your country, and you never know, once life progresses she may even see the benefit in sending the child to school in your country and anythign could happen.
The best advice I can offer you right now is to be calm, provide well, consider the mother has alot on her plate as she does all or most of the child care and so a small thankyou incentive to her once in a while will not hurt.
Be a good father, be a good provider, you can do both of these things without being a mug or taken for a ride, it is not a war or a competition, it is a situation you as adults need to consider before reacting to anything and everything that comes along that you like or dislike. Always take time out before reacting to any situation you feel is unfair, there will be many of them.
Good luck.