Someone was posting about this at the .com site.
In his particular case the ultimate trigger was a statesman from another family with an ambition of 3.
But quite a few posters say there's a lot of randomness to the civil war trigger.
here's the thread if you want to read it. The discussion gets better a few pages in.
http://forums.totalwar.com/showthrea...ger-DISCOVERED
From the ingame Encyclopedia
"in a tribe or monarchy any show of weakness may be challenged, again leading to civil war."
"high ambition can lead to a bid for power through civil war"