Admittedly I'm not much into this style but I have watched videos involving it. It seems to me that most doms take turns or there is a "leader" for the night. In all of the videos I saw they would both issue commands but were careful not to have conflicting orders and then the "backup" dom would make sure that the original rules that the "leader" had set weren't broken so that the "leader" could focus on the situation at hand.
Again, most of my experience comes from videos, so I'm probably not the best one to give advice but I would say they should rotate or trade off who is the alpha for the day/night/however you think would work best for you.
"Regret for the things we did can be tempered by time; it is the regret for the things we did not do that is inconsolable." - Sydney Smith
Kyle: 26 year old male
Katie (rymmare): 24 year old female
Kids: girl: 4 years old, boy: 2 years old