Let’s talk about what makes bickering between household dogs likely—dogs are more likely to fight if they are:

• The same gender
• Of a similar age
• Of a breed that has been bred to fight, guard things, or kill small vermin (pit bulls, working breeds, terriers). Fights are less likely among hounds and hunting breeds that are traditionally kenneled and worked together.
• Lack of frustration tolerance:  i.e. a short fuse
• High arousal/reactivity
• Genetic tendencies: we all inherit some of our personality from our parents and some lines of dogs within breeds are more prone to fighting

So, Ally and Ranger have some definite points in favor of their relationship: Opposite gender, big difference in age, Ally is from a breed with less of a tendency to fight.  
 
There are various schools of thought on helping dogs within a household live peacefully together. The most popular are:
 
1. Let them work it out.
This concept has been popularized by Cesar Milan’s enormous dog pack on The Dog Whisper. If your pack has a benevolent leader, this can work out nicely. However, if your alpha dog enjoys being a bully or has a short fuse, it may not work so well. It can also be impractical to have other dogs teach your dog some manners since most of us don’t have access to a huge pack of dogs.
 
2. Support the alpha:
Nicholas Dodman, DVM (Tufts Vet School faculty, author of “Dogs Behaving Badly”) is a proponent of this idea. The challenge is that it is often hard to determine which dog is the alpha. Often the dog making all the noise is not the one that is in charge. Owners also struggle with accepting that the underdog will be bullied.
 
3. Be the alpha:
In their booklet “Feeling Outnumbered” dog behaviorists Karen London Ph.D. and Patricia McConnell Ph.D. say: “Most aggression in social groups of species like humans and dogs seems to be in “middle management”. So your responsibility as the human CEO is to make it clear to your dogs that they will never be climbing the corporate ladder. If there are no vacancies at the top, there is no reason for them to compete among themselves. This is the approach that I take with my dogs and with clients who have dogs that are bickering. If your dogs only ever get what they want by being polite instead of competing, there is no reason to fight.
 
Here’s how I apply Patricia McConnell’s rules in my house:

• Don’t use your mouth to do anything I wouldn’t allow kids to do with their hands. Wrestling is fine. Licking ears for an hour is not.
• Don’t take each other’s stuff. When a bone is on the floor, it’s up for grabs. When it’s in one dog’s mouth, it belongs to that dog.
• Don’t block each other from going up stairs, through doors etc.
• Don’t push each other out of the way to get attention. Take turns as requested. I’ll say “Ally’s Turn” and pet Ally for a bit. Then stop and say “Ranger’s Turn” and if Ally continues to pester I’ll send her to her bed or out of the room.
• Stop rough housing when you are asked or you will get kicked out of the room or outdoors.
• Wait for permission to go out doors rather than shoving past each other or me.

More about Ally and Ranger:
Part of the reason I chose to adopt Ranger is that he and Ally got along so well when I introduced them at the shelter. He respected her warnings not to play roughly and instead they danced around without making physical contact.  From the very beginning, I was happy with their interactions with just each other. But Ally was clearly jealous to be sharing her people. She can make Ranger back up ten feet by just giving him a quick dirty look if he comes near when I’m petting her.  If I let Ally have her way, Ranger would get no attention at all.
 
Although Ranger is very patient with Ally, he does outweigh her by 50 pounds and if he lost his temper, it could be a problem. This did happen early on: I feed my dogs in separate rooms out of long habit and I’ve always had dogs who ate at about the same rate, but Ranger is a slow and messy eater. Ally quickly figured out that there would be dropped kibble all around his bowl and when she finished eating she would sneak in and grab a few pieces. Ranger seemed unconcerned about this, but I didn’t think it was a good idea and I kept meaning to change the eating set up… However, one morning before I had a chance to change things I heard a roar, a scream, and furniture knocked over. I ran over to find Ranger standing over his bowl breathing hard with an armchair knocked over nearby. Ally was standing outside the room shaking. Luckily, no one was hurt and they continued to get along, but it was a wake up call to do a better job as dog mom to prevent this kind of nonsense. I moved Ranger’s bowl to where I could watch more carefully.
 
I certainly don’t expect my dogs (or anyone else’s!) to go through life without ever getting irritated and raising their voices (i.e. barking or growling) at each other. But I do expect them not to routinely bully each other, not to hurt each other and to act politely most of the time. They do alright on their own for the most part, but I’m careful to keep the peace by having rules in place for situations where there might otherwise be conflict.