Dominate is probably the wrong word. More like help guide the new Star League. Keep in mind that preservation of the Hegemony, i.e. the Star League was the central tenet of ComStar. There was definitely some drift over the years, but protecting a legacy was the guiding gist of it. Of course, it was a direction subject to human frailty, layers of religious indoctrination and increasing paranoia as the years passed.
Just a real generalized definition, but you get the picture.
So entering the Second Star League from a position of equality and security, bearing gifts and the strength to protect the Inner Sphere from invading aliens was what the WoB had worked towards for over a decade (maybe longer.)
Having that dream ripped so close to grasping it caused their bloody knee-jerk reaction.