I prefer to get more information about the OP's personal behaviors affecting the dynamics in the relationship rather than assuming he's doing everything right and she's the evil one who needs to be trained to respond. She may just be reacting to his behaviors, that have nothing to do with power dynamic. He did admit that he's no angel. I'm more curious what that means.
It could be very true. Nobody is. The baseline dynamic remains she yells -> he gives. Whether that yelling has been triggered by him remains in question, but that cycle needs to break at any rate.
Even if he's an ******* triggering the whole thing, him pulling away attention will trigger a shift and a conversation that can yield results - but only on an even, honest playing field.
The point is not to train her, it's to break any unconscious conditioning in both of them that reinforces a negative stimulus/response cycle and force an intervention.
Let me give you a real example of mine, that I've used before: my wife asking me to vacuum. She asked me, so I did it. She then came up, "supervised" me, and criticized the job - by pointing out that the 'lines' in the carpet weren't straight. I had never noticed before then that vacuuming left lines in the carpet. I said I didn't care about the lines, she asked me to vacuum so I was vacuuming. And successfully getting the carpet clean. She insisted I was doing it wrong, that I didn't know how to vacuum properly, and insisted I started doing it right.
So when she started being aggressive and rude about it, I dropped the vacuum and walked away. This of course made her very angry.
When she tried to express that anger to me, I refused to engage with her about it. When she calmed down, I used the conflict to set some ground rules: you can ask me to do something, or tell me how to do it, but you can't do both. To me, vacuuming is about cleanliness. To her, it was more. So... when I vacuum now (rarely - it's now a 'pink' job), she leaves me to it, knowing I'll get it clean but not look the way she wants it. If she wants it that way, she can do it herself, because that's reasonable
What she can't do is screech at me and just have me running around making her happy as a consequence. We tried that relationship style, and it didn't work for either one of us. But the more I ran around responding to that stuff, the harder it was for her to see it was unreasonable, and the less I listened to her valid criticism about the stuff I was or wasn't doing... because all I heard or cared about was the screeching.
But you have to be unafraid of conflict to get there. The one that is more unafraid of conflict usually wins the conflict - and that was certainly my wife. Until it wasn't.