F. RENUNCIATION FOR MINOR CHILDREN
Parents cannot renounce U.S. citizenship on behalf of their minor children. Before an oath of renunciation will be administered under Section 349(a)(5) of the INA, a person under the age of eighteen must convince a U.S. diplomatic or consular officer that he/she fully understands the nature and consequences of the oath of renunciation, is not subject to duress or undue influence, and is voluntarily seeking to renounce his/her U.S. citizenship.
http://www.travel.state.gov/law/citizenship/citizenship_776.html
I'm sorry to hear that your relative is having difficulties regaining Australian citizenship. I hope the person will succeed, since this is what they want.
That’s not adoption that you referred to. When a child is adopted, the US statutes refer to laws that stem from treaties.
You are looking in the wrong area. The law you reference is written to protect children from actions of parents that emigrate.
The laws that govern adoptions follow from treaties that account for citizenship of the newly adopted child.
Apples and Oranges.