I believe it is simpler than that.
1. SAD is knocked up by FMD before she goes to HI.
2. BHO, Sr. is about to be forced out of school in HI because he is too old for the Kenyan government to continue his stay. (he lied about his age)
3. He concludes that if he had a US wife he might be able to extent that. FMD’s wife pays to help, so she will not have a B_tard child to deal with. There is no record of a marriage between SAD and BHO, Sr.
4. SAD meets with a local HI Doctor with Grandma Dunham. They arrange to her to go to Canada to unwed mother’s home and have the baby. They sign the necessary papers for adoption and the other option of keeping the child, but the doctor agrees to not submit them until the baby is born.
5. SAD goes to Canada, has the baby and the defiant child that she is decides to keep the baby. Contacts Gradma Dunham and tells the Dr. to submit the late birth paperwork. They fail to submit the required papers and the submission is never acted upon. So BHO, Jr. or whatever he was named is given no COLB from HI. The application was on file, but it was never approved.
6. SAD & BHO, Jr. (or whatever he was called) go to Seattle where she attends college.
7. No trip to Kenya, No return to HI because the paperwork is already signed undated.
8. Now we have the issue of the missing marriage document, how could she get a divorce without a marriage document. That is where Kenya comes in. BHO, Sr. supplies the document, which has later disappeared. The phony trip to Kenya is about a marriage document in order to allow the divorce papers to be processed.
9. From this point on the trail is tougher, because the Spooks are in the game of altering the records. What a mess.
Your story is fascinating. I have heard mention of a Canada connection with reports of birth listings for August of 1961. That is an interesting thing to explore.