Second you ignore once again the Kenyan father who would have to acquiesce to his son living in the USA.
You also never answered what evidence is there that Obie was born in any hospital?
My bad. I missed the fact that the code was Amended in 2000. So you are right, Obama Jr. would not have become a US citizen automatically upon establishing residency in the US if he really was born in Kenya. His mom would have had to wait five years before applying for his naturalization.
That still doesn't establish a motive for her to fraudulantly register his birth.
You speculate that she did it in order to make sure his dad could not take him back to Kenya. That makes no sense. Surely if he had actually been born in Kenya, his dad would have known about it and would be able to produce proof. Therefore, if she really had fraudulantly registered his birth in the US, he could easily challange that registration if he thought doing so was in his best interest.
So I really don't see how you have a point. There's no way they could have pulled one over on dad by fraudulantly registering his birth.
My original point thus stands. There was nothing to gain by committing fraud to register his birth. Obama's mom could have easily obtained US citizenship for him legally even if he had been born in Kenya. It would have taken 5 years, but so what? The fact that she was a US citizen gave her access to all the welfare programs she would ever want.