How should I proceed with wife and son's J2 visa

J-2 visas are given in the discretion of the consular officer, and there is a presumption of immigrant intent which must be overcome before such visas are given. Perhaps your wife can make another application with the embassy and bring all proof that she has many ties and bonds with Jamaica which would incentivize her return after her temporary stay in the US. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.