When I looked at this whole situation, I didn't ask myself why it was chaotic. I asked myself why not. My guess is that you two are not on the same page with your parenting strategies. You're not on the same page because one of you is pretty harsh and the other one is not, and that's at least your opinion of one another, correct?
This is not rocket science, although it is a big and steep hill. The problem is that you two don't have the same philosophy about what is reasonable to expect from these children. You yell at them because you get frustrated. You aren't consistent, and they recognize that they can get something from one of you that they can't get from the other. Children will exploit this—not some of the time, but all of the time.
So what you two need to do is go away by yourselves. You need to sit down and say, okay, here's what we're going to do. This is going to be the standard. We're not going to yell at these children. We're not going to hit these children. I don't think you spank them, which is good.
Bill Cosby's good ways to discipline without spanking
But you need to recognize that one of you needs to support the other no matter which one is in the window at the time. And be totally consistent. These children need to be able to predict the consequences of their actions 100 percent of the time. They need to know, if I do "A," I get this result. If I do "B," I get this result. Appeal to their greed. Tell them, if you want what you want when you want it, which is how kids are, then you just need to do the following behavior. They are trainable, and they will learn. The question is, are you?
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