The verdict is still out on the exact structure of dog pack hierarchy. The idea that dogs follow a linear unyielding pack order was conceived from the inaccurate study of wolves in captivity done over a half century ago.
Most scientists agree however, that canine hierarchy is much more "fluid" than the wolf pack model that has been the accepted ideology for decades.
Your dogs' may have one order when they're inside and a different order outside. One dog may be dominant around toys, and another is dominant when the coveted resource is food. Even this can change depending on the dogs' needs and motivations at the time!
Dominance = Priority Access to Valued Resources
Dominance is not a personality trait, rather it's the state of a relationship with another dog or human. If a dog is dominant with respect to another dog, then he has more access to valued resources. If a dog is displaying dominant overtures, then he wants more access to the resource.
This is one of those misconceptions made by owners. They usually feel like the dog making the big ugly display of aggression is the "top" dog, but a true leader is calm quiet and confident...no need for all that bluster & bluff!
It's the "wannabe" who makes the most noise.
(Sound like any bosses you've had in the past??)
Priority resources according to a dog is anything they need (survival) or want (pleasure):
Safety, food, high value treats (bones/chewies), toys, space (personal and territorial), people (owner), sleeping & comfort areas (the couch or bed), attention/petting, and other motivators such as tug or fetch, etc.
Your role, as the human in the household should be to dole out these resources. You are the keeper of the resources, which therefore makes you 'Top' dog.
I have the 'stuff' - Me boss!
You want the 'stuff' - You follower!
I know...that's probably a bit simplistic but it really does not need to be difficult.
The canines in the household should be informed that ALL of the highest rankings have been taken by you and the rest of the family including your children (and cats). This should make it easier on you and them. By simply taking the "lead" role from your dogs you will almost immediately start seeing a calmer, better behaved dog or group of dogs.
How do you do that? For starters, you don't follow the old advice of giving food and attention to the "Alpha" dog first. That only reinforces your dogs' to be bullies. And really, do you think because your dog exitedly runs through a door first he sees himself as king of the castle...or could it be something much less sinister as- he's JUST excited to experience 'what's next!'.
That certainly doesn't mean it's fine for your dog to blast through you at will, to the contrary,
let's teach them some:
Foundation Manners and Attention, Focus & Self-Control
I don't care if my buddies go through the door first, eat first or get on the bed...as long as I've given them the "OK" to do so.
Teach your dogs that speedy compliance to your cues (commands) gets them good "stuff" (remember the resources).
Great things happen by being polite and nothing good happens by being pushy with your family, guests or each other.
Welcome to effective, calm & enjoyable 'dog' leadership.