Square Root: There is no evidence the Obama’s mother was anyone other than the woman who he said was his mother. And she was not legally married to the father (American law doesn’t recognize the validity of a man’s marriage if already has a wife, no matter where she lives). It is irrelevant where Obama was born, since he was clearly a naturally born citizen (by right of birth to an American, regardless of where) which is what the Constitution requires. The fact that he married a Christian, ate pork and drank alcohol, and raised his children as Christians strongly suggests he was not a Muslim. He does apparently have a halachically Jewish half-brother, which was the closest to having e a president with Jewish relations until Trump (who has a Jewish daughter and grandchildren).
It should be noted that unlike his father (or President Trump), President Obama’s personal life (unlike some of his policies) has been beyond reproach.