She stated the child does not want to go.It's best that the child stays with the father,he will have a better life.
You don't know that, anymore than we know what the mother will do.
I'm wondering what was promised to the mother in order for her to give her consent. I find it suspicious that the op accuses her of abuse in another thread, but then would have agreed to send the child back to her for extended visits.
Sorry, OP, you really shouldn't be the one to put yourself between the mother/child relationship. She is going to be his mother forever, and there is no gurantee how long you'll be the step-mom. If you really have bonded with the child, call mom to thank her for letting him come. Flatter her, fake it, lie, just be nice. Don't ever let the child hear you bad mouth his mother, and don't allow him to either.
In the long run, the legal solution in the DR is never the practical one. Make nice with the mother. You're unsure of him staying, make it a family vacation of two weeks, get mom to meet you--get her out of her element and give her just enough access for bonding, not enough to take hiim. And if you do love the child, you wouldn't begrudge helping out momma--make sure she has enough to eat, etc. I know she'll use it for other things, but you will always be able to tell the child that you tried to help her.
So take precautions, as it seems prudent to do so, but find a way that doesn't cut him off completely from his mother.
And custody documents usually don't include a statement that says, "if the child wants". From personal experience, children are somewhat fickle on why they will or won't see another parent, sometimes very legitimate, other times based on who has more favorable rules (or lack thereof), better junk food, more cable channels, etc.
Sorry, OP for more "non-legal" advice. There are no gurantees, for sure, as to outcome. But I'd encourage you to search for a middle ground. That, more than the law, will help you in the long run.
Best of luck to you.