Can child have residency with only one parent's permission?

The question will be whether your fiancée has custody over the child. If not full custody, the American consulate or embassy may request proof that the ex-husband has given permission for the child to settle in the States. I'm not aware that the US has any type of agreement to send children back to the home country, but there is concern that the rights of parents be protected.  Due to the limitations of the Lawyers.com Forums, Alan Lee, Esq.'s (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.