Obama was in the legal custody of Catholic Soc Serv and the physical custody Madelyn Payne from 1971 to 1979. Stanley Ann and Lolo were stripped of their parental rights until 1979, Obama’s 18th Bday. Stanley Ann and Lolo divorced in 1981 and claimed Obama as an adult dependent upon them for education expense.
Even if those things happened, none of that would change the birth certificate. For instance, Madelyn Payne was not changed to the mother on the BC because she had custody.
If the BC that claimed BHO as the father, Honolulu as the city, Oahu as the island, Aug 4, 1961 as the date, male as the gender, and Stanley Ann Dunham as the mother was legally valid - determined by a court in 1971, as you say - then Onaka would have had to verify those things. Why didn’t he?
And how would we know if those things had really happened? What evidence is there for those things?