It does seem
to me you are only reacting to Ivy's bad choices, so she really is not the
submissive one, you are. Right?
No, I disagree. What you're describing is a human's ideal of "dog dominance". Think of it like this: Dominance is used to DIFFUSE tension and KEEP order. Dominance, in its most natural form, is meant to keep inventory of resources - to prevent scuffles, to ensure that the members of the pack get their share. That is how one should view dominance. But when you try to extrapolate and say a dog is "dominant" because she's trying to manipulate the situation by making me react to her bad choices? That's taking the dominance concept a little too far.

She is not voluntarily choosing to react "badly" to make me submit to her, to make me react to her. Here's where I think CM followers and +R followers dissociate: Aggression/Reacting is NOT a completely voluntary choice. When dogs aggress and react, they are acting so due to knee-jerk, primal reflexes, usually fear, excitement, etc. They have attached a strong emotion to that trigger and, when they see the trigger, they are working with their instinct. They have literally entered another state of mind. If you've worked with a lot of aggressive dogs, you'll see their eyes harden, their muscles tense and quiver, their jaw muscles tighten, their focus on you severely decreases, etc. These are not voluntary actions. They are the result of a strong emotions tied to the trigger. So to rid the dog of the aggression, you have to change the base of those emotions. Essentially, you have to neutralize the trigger, which is most attainable through DS and CC (desensitize and counter condition).

The Premack Principal is a type/method of human conditioning.
All conditioning holds true for all animals, including humans.
Premack's Principle is a psychological principle. It was derived from a study of monkeys, not humans. In fact, a large majority of psychology's most major, fundamental principles have been derived from animal research, including Pavlov, Skinner, Harlow, etc. How can one claim that those principles are only "human conditioning" methods? If you've done "come-and-go" training with a dog, that's Premack's Principle right there.