Bear in mind that Barack Sr.'s family was not poor. They were influential in Kenyan politics, and apparently were able to support him in college. Not very many foreign students studied in the US in that era, especially not very many Africans. In addition, there may have been youth discount fares available in some situations of which Ann could have taken advantage.
Sr. had backers. It wasn’t his family who paid.
Onyango Obama worked as a cook for USIS staff in 1959. BO, Sr. attended UH on a scholarship and his expenses were paid through the efforts of international literacy expert named Elizabeth Mooney Kirk.
None of the Obamas were involved in Kenyan politics. The Odingas, with whom BO, Sr. allied himself years later as a government employee, were Luo, and therefore possibly distantly related to the Obamas.