More likely scenario:
Teenaged Ann was seduced and gotten pregnant by Frank Marshal Davis, Grandpa Dunham's good friend (and probable Communist Party cell leader).
Davis is married, and therefore cannot marry Ann (besides being much older). Grandpa Dunham refuses to allow Davis to get into trouble over this, and convinces Ann to quickly marry Obama Sr, one of the few blacks on the island. Obama agrees because this way he gets citizenship eventually. Madelyn is upset but goes along.
This is why Grandpa brings Barry along so often to meet Davis -- because Davis wants to see his biological son.
When Barry is older, Davis pulls strings of his old black radical friends to help Barry get into Harvard, and then set up in Chicago with the help of radicals like Ayers and Jarrett.
Entirely reasonable and well thought out.
I’m thinking Ann had a one night stand with some sailor and the Dunhams paid off Senior to marry her.
My thinking is that if your daughter got pregnant by a man twice her age you probably wouldn't want him around. You'd move away sooner than have him in the picture. So FMD would only be around if he wasn't the father.
Of course it's possible FMD was the father and that as time went on grandpa started to feel closer to Davis and relented, but I'm thinking the Dunhams would have moved again away from Hawaii long before that happened. You also can't assume that in pre-Internet days you can't assume grandpa would have known about Davis's dirty novel or possible attraction to underage girls. He might just have been the only educated Black man the Dunhams knew on the island
Davis had pull at Harvard going back to his Chicago Communist days? Not sure about that. Hawaii was pretty far from the rest of the country and Davis pretty isolated. Hard to cash in on connections made 40 years ago if you don't keep them up. And I doubt his party friends made it into Harvard or the Saudi royal family.
Obama moved to Chicago to get in touch with Davis's or Ayers's friends or roots? Maybe. It's possible. But Chicago was also Alinsky's home town. Alinsky was dead by then, but if someone really admired him and his work making a trip to the city and dropping his name might open doors.
Chicago was also one of the really big centers for African-American politics: first Black Congressmen after Reconstruction, a Black Mayor before New York, a larger percentage of Black voters than Los Angeles, not as much a basket case as Detroit or Newark, not as Southern as Atlanta or New Orleans. It might have looked like a natural place for an outsider to break into Black politics.