Have you ever had to live or work with someone you didn't like? Think of the things that made the process a bit more bearable for you (time apart, everyone in their own space, less stress in general, focusing on other things, etc..)
Those same things might also help pets who have to live together.
But before we start talking about that, lets look some other issues or cautions
Note: Work with a certified behaviorist (or maybe even a vet behaviorist) on the below choices/scenarios
1. Are the fight injurious? Are there children who might get in the way? Are the fights escalating? Complete or partial separation might need to be considered while evaluating the relationship
Complete separation: https://www.facebook.com/groups/20444826822/permalink/10153138927526823/
Partial separation: https://www.youtube.com/watch?v=fKsYPaaahzQ&index=7&list=PL70eA_MZvAVor5I76KRvqyiuqLL7jRWhe
2. Medical evals for everyone - Humans and non humans
A pet in pain might be "cranky"
If a pet has a medical problem, it can affect how how other pets treat him/her
If a human has any issues, it could cause the pets stress and that stress can show "crankiness"
Medical evals might includes checks for physical or mental issues
Kidneys, liver, heart, thyroid, joint pain, dementia, anxiety, etc..
3. Can the relationship be rebuilt? Work with a skilled behaviorist on desensitization and counter conditioning. (DS/CC) Make the sight of the pet something to look forward to for the other pet. This can be difficult if there are resource guarding issues or if it's hard to get a good distance from one another. But a skilled behaviorist might be able to help work something out.
One example at this link: http://www.stubbypuddin.com/2014/04/dog-doesn-t-like-new-puppy.html
Skip down to the numbered list about half way down the page.
This process would need be modified depending on each individual situation
See more on DS/CC here: http://www.stubbypuddin.com/2014/12/advanced-counter-conditioning-and.html
4. Well proofed cues
Having some things in place like go mat or go to crate can be quite useful when one pet is giving the other the "evil eye"
Try to stop an argument before it starts by calmly asking everyone to go to their places
Make the training fun. Train during boring times then slowly increase distractions. So the behavior will be in place when needed.
Looking for a "tell"( figure out what the pet will do before he/she does it)
The value of mat value: https://www.youtube.com/watch?v=WmVitwA13pU
Teaching "Go To Mat": https://www.youtube.com/watch?v=tVGaslyGaGE
Also see everything by Leslie McDevitt (Control Unleashed books and DVDs) for info on the usefulness of mat value
Building crate value: http://www.stubbypuddin.com/2015/02/crate-acclimation.html
Important - Don't send pets to their places as punishment. Make going to place a fun thing
A pet who is growling/hissing or lunging or barking or even biting or scratching might be showing discomfort with his/her situation.
I don't recommend timeouts for a pet who is trying to communicate
5. Jolly talk
The may or may not work in all households. But if you see tension, try laughing or jolly talking, or initiating a game of play - just something to diffuse the situation. Try to do this before things get too tense. I do some jolly talking in this video (also posted above): https://www.youtube.com/watch?v=2sNHqOonwYA
For more on Jolly talking, see http://blog.mysanantonio.com/latrenda/2013/10/jolly-talk/
6. Stress Reduction and Relaxation. As mentioned at the start of this post. We can deal with bothersome people a lot easier if there aren't other stressful things in our lives.
So try to look for ways to reduce the stress in the household: http://www.stubbypuddin.com/2013/12/stress-reduction-for-behavioral-issues.html
And informally: https://www.facebook.com/groups/20444826822/permalink/10153031812756823/
Work with each pet individually to keep their minds focused on something other than the sibling they dislike
Calm sniff walks
Fun trick training
Scent games: https://www.youtube.com/watch?v=ElGbNnnIFWc&list=PL70eA_MZvAVpN5SFukOeB2k2CM15mf8Vd
7. The loudest and/or strongest isn't always the instigator. Just because one pet charges or bites or growls or hisses doesn't mean that was the pet who has the issue. If you are not sure which pet is causing the issue, work with each pet individually and evenly.
Teach well proofed cues to both pets, send both pets to their crates or mats, etc..
8. If it's safe to do so, reward everything that is not arguing or fighting or staring or snarling. i.e. see the pets sitting calmly ignoring each other, then calmly give both a treat. See pets calmly sniffing each other's butts - praise and/or treat. But work with a skilled behaviorist. If there is tension or resource guarding, a treat could make things worse.
Info on finding a trainer here: http://www.stubbypuddin.com/2012/09/hiring-training-where-to-start-your.html
Other links that may or may not be useful
Growling/Hissing Is Good http://www.stubbypuddin.com/2014/02/growling-is-good.html
Trigger Stacking: http://www.stubbypuddin.com/2013/11/trigger-stacking.html
Bleeding Backwards Through Time: http://www.stubbypuddin.com/2011/10/bleeding-backwards-through-time.html
Multi pet household safety: http://www.stubbypuddin.com/2013/09/multi-dog-household-safety.html
Loose Leash Walking: http://www.stubbypuddin.com/2014/07/loose-leash-walking-summary.html