Barack Obama Sr. was a Muslim and it is a Muslim tradition to give birth in the parents' home which would have been in Kenya.
http://www.nagpuronline.com/people/rit_mslm.html
Rituals And Cerimonies
Muslim: The rites and ceremonies observed by Muslims chiefly consist of those as relating to pregnancy, birth, naming, sacrifice, initiation, betrothal, marriage, and death,
Pregnancy: In the seventh or ninth month of pregnancy a fertility rite may be performed as among the Hindus. The woman is dressed in new clothes, and her lap is filled with fruit and vegetables by her friends. In some localities a ceremony to propitiate the spirits of ancestors is performed.
Child-Birth: A woman goes to her parents home after the last pregnancy rite and stays there till her confinement is over. The rites performed by the midwife at birth resemble those of the Hindus. When the child is born the azam or summons to prayer is uttered aloud in its right ear, and the, takbir or Muslim creed in its left. The child is named on the sixth or seventh day. The proper name for the male child is often formed by combining the prefix abd or servant, ghulam or slave, or suffix baks or 'given by' to the numerous titles of God. e.g. Abd-ul-Aziz, Rahim, Razak, Ghulam-Hussain; Khuda-baks Hyder-baks, etc.
“We have had a lot of people on this thread ask sarcastically Why would she go to Kenya to give birth?
Barack Obama Sr. was a Muslim and it is a Muslim tradition ...”
His mother was an iconoclast, an atheist and a progressive. She would have no reason to follow such traditions.