You can help prevent these disagreements by recognizing the highest ranking dog in your pack and favoring it with your attention. This is the dog you should pet first, feed first and let out the door first. Giving alpha dog privileges to a lower ranking dog, even if it might be your personal favorite, confuses the others and can lead to fighting. All the dogs will be more secure and comfortable with each other when they're clear on where they stand within the pack. There are some dogs that just aren't going to get along no matter what.
Some breeds are less sociable than others and some are known for fighting.
In these cases, a permanent separation may be the best answer. This doesn't mean you have to get rid of one of the dogs. One dog spends part of the day with the family while the other dog is crated, outside in the yard or in another part of the house. It's not as cozy as having all the dogs together but can be a very workable solution. Obedience training for all dogs in the pack is highly recommended.