His marriage to African bride would have been recognized. HOWEVER, there are many articles on the web about problems that have taken place in Kenya when the tribal marriage wife shows up at the door to stop a new wedding..and some of these have landed in court.
Obama’s marriage to Ann - even if it was legal in the US (and it wasn’t legal)..still would not have been recognized in Kenya..and that is the root you look to since Sr was Kenyan. It is a convoluted mess.
I know that Islam allows up to 4 wives at a time. I’m wondering if Kenya would have any problem recognizing both marriages.
But I think Obama (and his mom) played the international peek-a-boo game all along. For instance, I think he was adopted by Soetoro in Indonesia but never told Hawaii about it so he could get benefits of being Indonesian (foreign student aid, for instance) AND benefits of being American. But I have no way of confirming or refuting that so it has to remain just a hunch.