Southern girl from the US dating a native Kenyan

In my opinion, there can often be a generational clash between older (more traditional) family members and younger (more westernised) people.  From what you say, I am guessing that he is the first born (oldest) child, in which case he will assume the mantle of family head, if his parents have died.  My wife is Kikuyu and is first born and also nominally the head of the family, as her father has died, but is hasn't really affected our lives at all. 

A first born male is, however more significant that a first born female and I imagine that some relatives would be expecting a child to continue the family line. 

I think it all hinges on your partners attitude to tradition.  I know of quite a few Kenyans who have lived overseas, who find that the demands and pressures from family too irritating - very often there may be an assumption that those family members who live in the west are loaded with money and they are looked to to sort out all the family problems - and they sometimes wind up cutting themselves off completely.

I think that the problems might start of your partner wants to return to Kenya and live there.  Its far more difficult to ignore the family, once you are here!!