What makes sense to me is that SAD is not the mother and there is no birth certificate with her name on it. Despite the divorce from Senior there is no paperwork to make Junior the child of SAD. We have no idea what name or citizenship he traveled to Indonesia with or when he returned. He could of used Barry Soetoro, Barack Obama, Barack Soetoro, Barack Toot, or some other name entirely, like FMD Jr. but without legal documentation to show who he is they, the Dunhams, needed the father who is listed on a birth certificate to give custody to the Dunhams, for what ever reason.
Junior shows up at age ~3 in the Dunhams care, for whatever reason. Where did he come from? Seattle, Boston, the Philippines?