Here's a rather unique and interesting situation from Autumn.
I adopted my dog from a shelter about 7 years ago when she was about 1 year old. She is a crossbreed, but definitely has strong herding instincts. She is generally sweet and calm around my cat, except for when the cat gets in trouble. If I raise my voice at the cat when he is chewing on the afghan, the dog runs over and smacks him. The cat is old now and I’m afraid he will get hurt. The cat hasn’t been hurt so far and the dog hasn’t escalated the discipline, but I would like to stop her from doing this. Any suggestions?
I would absolutely love to see a video of this! Yes, part of the reason is that it would allow me to have a better idea of exactly what is going on. But to be completely truthful, I think this would be one of those videos on YouTube that goes viral!
Dogs don't mimic human disciplinary actions the way that our children or even apes might. Dogs also don't associate cause-and-effect in the same way that we do. So it is unlikely that the dog is consciously seeing herself as a "disciplinarian" or somehow punishing the cat for you. That is especially true if you have never struck the cat yourself (based on your concern I assume you haven't).
What is more likely is that your raised voice is triggering excitement in your dog, and that is leading to the behavior. She hears your own anxiety or excitement and sees your body language. When you raise your voice it triggers even more of a heightened excitement state in her and is the trigger. If you've been around herding dogs you probably know that they can become worked up quite easily and have a low threshhold for such triggers unless they are specifically trained otherwise. The cat is likely just the outlet for this behavior and it could be directed towards any nearby pet if you had others.
There are a few things you can do. First, change your own behavior. Instead of yelling at the cat make different noizes. Air horns can work well, though they are particularly loud. You can also put coins or small rocks in a used metal can and shake it vigorously. Any sudden, loud noise is generally sufficient to startle a cat out of its behavior. And such noises don't come from a human so your dog may not react the same way. An alternate is to have water guns placed around the house and whenever you see the cat doing this simply give him a good squirt. This has no noise and is a highly effective training tool.
You can also work with your dog regarding those vocal tones. Use methods similar to what hunters do to desensitize a dog to gunshots. Start with her in a quiet place and give her a command to sit, lie down, or stay. Then make a soft yell or shout. If she gets up, make her go back into a stay or hold position and reward her. If she doesn't get out of that position, give her a bigger reward. Do that for several minutes every day, and after a few days raise the volume and urgency of the shout. Only reward the good behavior of being calm and still, and don't get mad if she gets up or runs around. At those times just make her go back to the beginning. The idea is to reward the desired behavior and gradually raise the intensity of the stimulus. When she starts to learn that a raised voice means she should be still you can start trying it around your cat.
Best of luck!