To be honest, I can't recall ever having read any sort of rules about making Charisma checks in this sort of situation.  It makes sense to me to use it with opposed Charm spells, but you're using Dominate, not Charm.  The daughter being magically made friendly towards the Brachina wouldn't even apply in this situation, I think, since you're just completely taking her over.<br/><br/>Now, if the Brachina then decided to cast a Dominate spell of her own, then I think some sort of opposed check would be called for, but otherwise, I think you just gain control of her.