"Dominance" is not a thing. Dominance theory is based on observations of a captive wolf pack that are now considered scientifically faulty. Beyond that, dogs aren't wolves. Wolves have an entirely different system of communication than dogs do, both verbally and body language-wise and have an entirely different relationship with each other and with people than wolves have with other wolves.
What was once considered "dominance" is now widely acknowledged as insecurity and lack of training.
When your CC pushes his way into your interactions with the Pit, ignore him. Teach him that being an insecure bully doesn't get him attention or affection. If he repeatedly interjects, *calmly* put him in another room or in a crate or wherever. It's not a punishment, or a time out. You're attempting to communicate that pushiness means getting ignored or having to be alone.
The basis of training should happen when the dog at home and not distracted. It sounds like you haven't followed through with your training in high distraction scenarios. To me, a dog who stays on command in my home is 25% trained. The other 75% is holding a stay in public, surrounded by people and dogs. Which takes months and months of dedicated work to achieve.