You have not addressed why Kezia would not have known Ruth existed until some FIVE years after Ruth arrived in Kenya a few weeks after the kenyan returned from the US in August, and married Ruth on Christmas Eve, 1964.
Your article clearly states that Kezia maintains she didn’t know about Ruth until she met her in hospital...and now you need to find just when he had his first major accident - WAS IT AFTER he and Ruth separated, but before he came to Hawaii in supposedly 1970, where an image with a christmas tree shows a walking stick.
Kezia explained it. BHO Sr. lied to her and left her in the family compound in the tribal village while he lived in Nairobi with a much “higher status” (in his mind, I suspect) white woman. I doubt Ruth knew about Kezia either.
BHO Sr. was a drunken, lying, narcissistic serial bigamist. I don't see the mystery.