Whether it’s sibling rivalry or two separate dogs, the way you go about solving dog housemate rivalry is the same. Either way, it’s very hard to resolve.
First of all, after a fight, you obviously need to separate the dogs for the moment. It’s best to have a crate so you can keep one dog in a safe place rather than tethering a dog who is then vulnerable to attack by the other dog. You simply rotate the dogs every hour or two, which keeps both dogs safe, at least for the moment. Beyond the initial day of the fight, you may need to muzzle-up your dogs, depending on how bad the wounds are. If it’s just nipping with surface damage, muzzling may not be necessary, but if blood is drawn, I would consider muzzling your dogs until further notice.
Next, you need to identify the triggers that caused the fight in the first place. Most likely, you are reading this after witnessing several dogfights over a period of time, which gives you more data to figure out what is causing the rift. As you can imagine, there are many possible triggers causing the mayhem, and it may be not just one, but several triggers involved. Usually, it’s one of the following: toys, attention, food, tight spaces such as doorways, visitors, sleeping space, and more. Regarding attention, I am referring to you, the owner. You, yourself, often can be the trigger causing your dogs to fight over the resource, meaning you.
Regardless, if you can determine what the trigger(s) is, you should start intense obedience training. It’s important that both your dogs understand who is the alpha, and that can be accomplished with solid obedience training. I recommend you train separately and do at least 20 minutes a day for a while. Reinforce commands such as sit, down, stay, off, come, touch, place, and leave it. Leave it can later be used to let your dogs know to divert their attention away from the other dog when it looks like one may be giving the other the “stink eye”, a precursor to an attack. Touch is a targeting command – you teach your pups to touch their nose to your palm – it’s a fun command that you and your dogs will enjoy.
Counterconditioning and desensitization – choose one of the triggers that you believe is causing the problem and tether both dogs near each other. If the trigger is a toy, a bone, or food, place it on the other side of the room, stand next to your dogs, tell them to look at the trigger, then reward them with treats. Over a period of of days or perhaps weeks, your dogs will begin to associate enemy + trigger = yummy treat. This will cause them to settle a bit when the trigger is within range of either dog.
If you happen to be the trigger, it’s very important that you show no exuberance when you first come home or when you are leaving. You should pay careful attention to your positioning in tight quarters such as hallways. You don’t want to favor either dog – in fact, you should use the commands you have been working on to get the dogs to simultaneously sit and stay, rewarding them both at the same time when possible.
If the above, after a reasonable amount of time and effort is expended, fails to resolve the fighting, does not yield a peaceful home, your only other option is to rehome one of the dogs. It’s tough, but it’s better than constantly crating one of your dogs and managing the quarrels.