Regarding the bigamy aspect, from what I’ve read, there is a lot of murkiness surrounding 0bama Sr’s marraige to Kezia, dates of their first son’s birth, when 0 Sr left for the US, whether they had a legal marriage at that time or ever, etc.
There are conflicting dates regarding Kezia in newspaper interviews and in Dreams Obama claims that only the children of the Ndsandjo marriage were able to prove their mother's marriage and to inherit from BHO Sr. I regard anything Obama says in Dreams as highly suspect.
What seems most likely to me is that Kezia’s tribal marriage was legal and recognized in UK Colonial Kenya under the Marriage Act of 1902 and that bigamy was unlawful under that act EVEN FOR MUSLIMS!
See Kenya Marriage Act of 1902 paragraph #49:
49. Whoever contracts a marriage under this Act, being at the time married in accordance with native law or custom or in accordance with Mohammedan law to any person other than the person with whom such marriage is contracted, shall be guilty of an offence and liable to imprisonment for a term not exceeding five years.
kenyalaw.org/family/statutes/...?file=The+marriage+act.pdf
The best account I have found regarding the Kezia-BHO Sr marriage is from the Daily Mail:
“Barack was also worried about what his father would think because I was so young, but he gave us his approval. He sent my mother and father 14 cows for my dowry.
“Barack’s father was only a cook so it was a big sacrifice. Very soon after, we were married.”
That was January 1957. Kezia and Barack Snr set up home in Jericho, a section of Nairobi created for government employees, and began a family.
First son Roy was born in March 1958. Kezia insisted: “Barack was a good husband.”
It was not long before Barack’s potential was noticed by his employees and he was offered a scholarship to the US.
By the summer of 1959, he was bound for Hawaii, leaving Kezia three months pregnant with Auma.
Kezia said: “I went with him to the airport. He gave me a cuddle and I was crying.
“He said, ‘Bye bye, see you later when I come back.’”
Instead, Barack Sr met Barack Jr's mother, Ann, in Honolulu. She was an 18-year-old fellow student from Kansas and within months they were united in what appears to have been a bigamist marriage.
Without proper discovery in a court of law and unfettered access to documents and witnesses in Kenya and HI, we won't know the legal truth of whether Obama was a UK subject at birth.