These problems are handled a tonne of different ways.
Some people let the dogs work it out, others set boundries and limitations to how they can work it out and others don't allow it at all.
I'm in the middle. I've set boundries that my dogs abide by. If one of them tries to steal a toy from the other and gets corrected APPROPRIATELY, I'll let it go. If the dog doesn't heed the correction, I will step in and correct.
There are some things that I do not allow at all, like correcting over food. I've trained my dogs to eat with their heads in their bowls never looking at the dog two feet next to them. If ever I see them eyeing the other dog's food, I'm right there with a firm verbal correction.
It's dependent on the dogs involved really. Hades is quite submissive so most of the time he gives in to Roxy's demands. And generally, Roxy gives corrections appropriately, not too much but enough to get her message across.
If it's clear that your dogs aren't on a level playing field when it comes to these corrections; ex) one dog OVER corrects the other, and the other dog never corrects the "dominant" dog for anything, than I would play a very active role in setting the boundries.
If you've seen any type of behaviour from the "submissive" dog that shows he can stand up for himself APPROPRIATELY when need be, I would stand down. Biggest, most importantly, is: Is the correction appropriate? If it's all out snarling, growling and mounting over who gets to go through the doorway, that's not an appropriate correction, I would quickly interevene and cease that behaviour.
If it's a low growl over a toy that the other dog is eyeing. I might watch to make sure the other dog listens, and let that go.
The other side of the matter is, if the dog doing said crime, is doing a crime that would require a harsh correction from the other dog, I step in. For instance: Hades used to ram Roxy, hard, and often. Roxy would correct him mildly the first few times, than she would really lay into him. Technically, her rough correction WAS appropriate, but I didn't want Hades to think that behvaiour was acceptable at all. So I stepped in from that point on, and he's stopped.
I guess this has gotten long, but what I'm trying to say is, it's kind of a personal choice when it comes to this matter. And a lot of things have to be evaluated before making your decision.
