If Obama's mother was not legally married, then a different provision applies:
Birth Abroad Out-of-Wedlock to a U.S. Citizen Mother:
A person born abroad out-of-wedlock to a U.S. citizen mother may acquire U.S. citizenship under Section 309(c) of the INA if the mother was a U.S. citizen at the time of the persons birth and if the mother was physically present in the United States or one of its outlying possessions for a continuous period of one year prior to the persons birth. The mother must be genetically related to the person in order to transmit U.S. citizenship.
Then why did you post the Section 301(g) excerpt at all?
By posting it, it is logical to assume, that you are using that as a justification for proof of citizenship.
Then, as soon as anybody points out the flaws to you, you duck and dive, and go in another direction - just like BHO - your story keeps on changing.
How about taking a specific stance and giving us the full monty of what you believe. No obfuscations. Think you can do that?
She was married. The divorce papers have been disclosed.