This is just weird. Mombass wasn’t part of Kenya in 1961.
Mombasa was part of Zanzibar until 12 December 1963.
Here's some further verification:
"Officially this coastal strip still belonged to Zanzibar until ceded to a newly independent Kenya in 1963."
The coast city of Mombasa was not technically part of Kenya in 1961 when Obama was born. It was part of Zanzibar. So why would Obama's father take his pregnant wife there to give birth and not to, say, the Kenyan capital city of Nairobi? You'd think he'd at least want his son born in his own country, if not in Hawaii? Why a coastal city, far from his home village and far from the capital, that was really part of Zanzibar?
For the same reason American men take their young mistress playtoys to Cancun or Bermuda or Aruba and not to Cleveland.
I think you're being way too anal about the whole thing. Your attitude reminds me of a funny "Far Side" cartoon I saw many years ago. There are two frames in the cartoon. The first frame shows an Indian village, where a drummer holding a big drumstick has been beating loudly on a huge drum, so hard, in fact, that there's now a huge hole in one side of the instrument. The other frame shows a circled group of covered wagons, with an anxious, frightened group of people gathered round their leader, who says, "Don't worry folks ... they only attack to the sound of the drums!"