Any theory which requires Ann to travel alone to Kenya is a non starter in my opinion. If Barack Sr didn't, go Ann certainly didn't go. It would take very good evidence to the contrary to persuade me otherwise.
Anns family may have helped to pay for her trip in the ultimately futile hopes that the Obama family would adopt and raise the child in the fathers Kenyan culture, with or without accepting the mother into the family.
I find no part of this suggestion reasonable from my perspective. What kind of mother would pay for her daughter's trip to an African nation where civil and racial unrest is prevalent? This notion strikes me as far fetched.
Ann and her parents were committed members of the Communist Party USA, and she was living out her ideas of what it meant to be a good Communist. The idea that she would only travel to Kenya with a chaperon is exactly contrary to the spirit and life she was dedicated to follow. Telling her she could not and would not do so would have been tantamount to a dare she could not ignore. In later years, she lived in places such as Indonesia without a husband or other chaperons to accompany her on her travels. So, there is no evidence to indicate she did not and could not have done so as a rebellious 19 year old ideologue.