Adjustment of Status under Section 13 of the Immigration and Nationality Act is available to A-2 aliens who performed diplomatic duties and their immediate family members. However, an A-2 dependent cannot apply under section 13 on their own. Thus, only your father as an A-1 alien engaged in diplomatic duties can apply under Section 13.
While written by an attorney who is a Florida Bar Certified Specialist in Immigration and Nationality Law, the statements herein should not be construed as legal advice. No attorney/client relationship has been created without a formal consultation with the attorney and the attorney has agreed to accept your case.