But why? Why run home to jump through these hoops? Why not just have the child naturalized if us citizenship is later an issue (which they might not have thought would be an issue, since mom was American). Even with the Kenyan birth, mom’s citizenship makes him a citizen, though perhaps not natural born. There would be no hurry to register the birth in Hawaii, so why would dad leave mom in the hospital (woman stayed in for about a week back then) and leave her in a strange country?
Do you really think they were trying to ensure that he be considered natural born in 1961? It just doesn’t make sense.
Naturalization would have been another issue. If born in Kenya, baby Obama would not be an American citizen at birth under the law in effect at the time. I presume he would have had to meet legal US residency requirements before he could have been naturalized some years later. There is no record, to the best of my knowledge, of a later occurrence of such a naturalization.
In so far as the time spent by mom in the hospital after delivery, the custom may have been entirely different in Kenya than in the US at the time. We can only speculate on why she would return to Hawaii so quickly after the birth, but one reason might be that she was supposed to come home earlier (to begin classes at the U of H, perhaps) but went into premature labor while in Kenya.