Babies have a habit of asserting themselves at inopportune moments. Perhaps Mombasa is where they happened to be when the birth process began.
There was probably a dearth of hospitals then in Kenya. I could certainly see them wanting a hospital birth rather than a village birth in case of any problems. That might have been reason enough for them to journey to Mombasa.
I'm not saying they should have had the baby in the village but Mombasa is very far from the village. Nairobi, the capital city, has many hospitals and is much closer. Do we think they were touring the coast, far from their home village, on a trip to Kenya while she's days from giving birth? It just doesn't pass the common sense test.