One does wonder, however, how it is the adolescent Duras son is able to get so many to follow him. Did these Klingons honestly think a child would make for a good leader? That he wouldn't be the visible part of a puppet regime being controlled by the Duras sisters?
I imagine the Duras sisters promised a lot of power to those who followed them, and were able to back that up with the clandestine backing of the Romulans.
It was established prior that there was a lot of corruption within the Empire, so it's natural that the crooked guys would follow the more crooked option.