I am not sure that a parent can give up a child´s citizenship. They can legally change a childs name and this may be where the bigger issue lies if Barry never legallychanged his name back to Obama. Also, if Barry used an Indonesian passport as an ADULT Bambi is indeep DU-DU!
A parent cannot give up a child’s US citizenship.
Relinquishing citizenship has to be done by the individual themselves and in very specific ways.