This is a very difficult topic. You have two or more dogs, and they are getting into fights. When is it time to find a new home for one of them?
I recommend re-homing if the quality of life for all involved (people and dogs) is drastically affected, even after trying well-executed training exercises. It is often best to hire an in-home trainer to assess the situation to see if it can be worked through.
Once an appropriate, positive reinforcement-based approach is devised, it is important to be diligent about executing the steps properly.
The steps should include desensitization of triggers that cause the aggression, management when not able to work with the dogs and more training and physical exercise to alleviate any possibility that increased reactivity is due to boredom. A tired dog is generally a more happy dog.
Desensitization of Triggers
A skilled positive reinforcement trainer will show you how to introduce stimuli to your dogs in a level that is low enough so it does not elicit an aggressive response. Triggers might include the presence of a food bowl or bone.
Management is a critical component of successfully treating sibling aggression. This includes coordinating feeding times so bowls are placed in separate rooms or behind baby gates so the dogs do not have access to each other. Also if fights have occurred when you are out of the house, dogs should be separated when alone.
Training and Exercise
This is very important to increase the chances for success. Bored, under-exercised dogs are more reactive, period.Hopefully with the help of a skilled trainer, you can help your dogs learn to live together peacefully.