Honestly feels like I'm fighting the battle alone. If it keeps going like this, I won't be surprised if she leaves, or if I have to actually swallow my pride and say, "It's over." I really want neither, and would like to see these problems be confronted, taken care of, us to be happy, stable, and see our marriage bless rocky marriages. But I have made my peace on it. If this marriage were to end, I would be ok. But I'd rather that not be the case. I actually do love her. I just don't love the way she feels the need to make me feel like.
Rebelling against Christ is swallowing your pride? The Proverbs warn repeatedly about a quarrelsome wife, but the Bible does not teach that being quarrelsome and rebellious is grounds for divorcing one's wife. Maybe it could keep you out of certain ministries, but not for divorce.
With her attitudes about sex, it seems unlikely that she is committing adultery on you. Why would you even consider the idea of the marriage being over.
I don't think you should have your wife leave the house to cool down. Kicking someone out of the house for something just sends the wrong message. Making her leave the house makes it feel like you are kicking her out-- in some foreign country. If you want to leave to cool down or to give her a chance to cool down, I don't see a problem with that as long as you tell her you are taking a walk or running an errand while she cools down and that you will be back. Anything that could be perceived as you leaving or you kicking her out of the home should be off-limits.
You are the man. You are the leader. You have to lead on this idea of no divorce. The idea of divorce shouldn't be brought up, like you wrote down in your proposed agreement. It shouldn't be tolerated. You have to get this option of things not working out out of your mind. Swallowing your pride would be living through this difficult mess until things get straightened out.
I wonder what Hosea's wife acted like around the house. At least it doesn't sound like you have any of these sexual unfaithfulness issues to deal with that he had to deal with. Just think of his assignment, the woman he had to be married to. If God gave you an assignment of being married to this woman, be thankful she isn't like Gomer, and do what the Lord has given you to do. If you choose to be married to a woman, God expects you to honor your commitment.
About your list of rules-- I think it is too long. Keep it simple. "No yelling." "No criticizing someone else's apology." You don't need an explanation for each rule. Do that verbally. If you keep it simple, she might just agree to it. If you put commentary on your list, you are writing a list of criticisms about her.
I still don't get why a woman may not be able to just make up right away after an argument either. You have to be realistic. Sometimes, they need some time to deal with their thoughts.
Don't let her beat you down and make you think her emotional issues are all your fault. Apologize if you do something wrong, but you aren't responsible for all of her anger issues.