I got married in Massachusetts 19 years ago and the man is from the Dominican Republic can he divorce me in his country

You should take him to court for child support whether in a divorce action or a separate support action. It makes no difference whether your marriage and/or divorce is legitimate if you are seeking support for your child. In any event, Massachusetts recognizes foreign marriages and may or may not recognize the divorce depending on the documentary evidence of marriage and divorce you have available.

This is a Jurisdictional issue. It depends upon where you last lived together to determine which country and/or state has jurisdiction over your divorce. If in fact you last lived together in the state of Massachusetts before separation and he unilaterally obtained the divorce, then I would recommend that you pursue a Complaint for Divorce for all issues including property division, division of liabilities, custody, support/medical, tax related matters and all other related matters. If not in the least if you and your children have resided in Massachusetts for at least six months than Massachusetts has jurisdiction over the children and support related issues. The Probate & Family Court has a Lawyer of the day program available in most if not all of the Courts, which can at least give you some direction in the event you are representing yourself. I would recommend that you go to the Register's office in the Essex Probate & Family Court and make inquiry regarding the availability of the lawyer of the day program.