is it difficult to get a visa (visitor or h2-a) when you have children in the US, but do not plan to marry the children’s mother (us citizen)

Visiting and H-2A visas are given in the discretion of an American consular officer based upon the officer’s perception of whether the visa applicant has sufficient ties and bonds with the home country and whether the individual will return to the home country at the end of the period of stay. In your case, it appears that the officer had the perception that you would remain in the US if he/she gave you a visa since you have children in this country. You can try again bringing whatever proof you have of your ties and bonds with the home country. 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.