This picture is several years old but it gives an accurate idea of the interactions I expect all members of my family to be capable of. Granted, Jenny is a good role model and Snuggers the cat owns that end of the couch...but I believe we should expect and train animals to get along.
Not that I run a perfectly interacting household.
This is Snugs and Breena; this is the most they ever interact and I'm a little surprised they walked away from each other without either smacking the other in the face. Breena doesn't really care to interact with dogs, or I should more accurately state, she thinks Gracie is too bouncy. And Gracie is too bouncy for most cats; but Gracie knows the difference between inviting a cat to play by bouncing at it and by making the cat a toy -- forbidden. I did not teach Gracie this alone - Jenny's example helped but most useful of all was Ellie. Ellie was a really lovely black cat who I pulled from a kill pen on her "last day." Many years ago in Canada....
Ellie firmly believed that the best way to teach a dog it's place in the world was to walk straight up to it, sniff it in the nose, then rub against it several times indicating that she owned the dog. Dog's were always so taken aback by her straightforward, calm demeanor while she carried out this behavior, that they would just stand there first stunned, then slightly uncomfortable. Ellie would then jump up on the arm of the couch or some other prop that put her at eye level with the dog and just watch the dog. At the age of approximately 17, Ellie passed at the end of this winter, about the same time Lil was born. Lil's upbringing will be the worse for not knowing Ellie. Cats and dogs can teach each other important life lessons.
Hmmm, maybe so far it seems what I'm really talking about is allowing cats to rule dogs. I think there might be some benefit in teaching dogs that all cats are to be treated with respect. I think the more powerful an animal is, the more it has to learn about reigning in it's behavior and physical reactions for those it shares a house and neighborhood with. I think it is particularly important for us to remember this when adding a new member to our family. If adding a young animal, think about the potential it is growing into. If adding an adult animal, think about how it will fit with the personalities already living in your home.
Size for example is not an excuse for poor behavior. I cringe every time I see a small dog lunge at children or adults, the dog's owner being under the impression that the dog is too small to do any damage or be held responsible for it's actions. Legally they are correct; it is the person, not the dog who will be held responsible for damages. From the vantage point of training however, small dogs can be trained to be just as respectful as their larger cousins. Just because you can pick an animal up does not mean you can forgo training it.
I believe that respectful interaction are the responsibility of the adult human in the household and begin with the tone that the adult human sets. I have found for example that the same is true in teaching college students. If I clearly develop and model an attitude of respect, verbally acknowledging respectful statements and actions, I develop a class where students treat each other with respect.
At home I also show respect and I praise successful interactions. In the classroom if someone is disrespectful they run the risk of being publicly called out in class on their behavior. At home disrespect leads to being isolated and ignored; only socially acceptable interactions allow an animal to remain part of the interactions. Sometimes time outs are necessary for animals so that they can regain enough calmness to again be capable of socially acceptable behavior. It is up to me as the adult human to set the boundaries of what socially acceptable behavior is. Modeling for people and for animals has to be different; animals react to how we physically move, our voices, and the type of energy we are giving off. They can read when we are nervous, sad, or finding their behavior amusing.
Keeping multiple species can be challenging. For years I had a pet rabbit who lived inside, where the action was. She had both a large cage that stood over the dogs and an exercise pen that expanded out allowing her to jump and run in the living room without being in danger of chewing electrical chords. Sometimes her activity was too stimulating for a dog -- Gracie's sister Kate for example needed to be crated while the rabbit was out. Rather than believing I could will Kate to behave I read her body signals. They told me she had a strong prey drive for something small and fast. I chose to not put the rabbit's life at risk. Know that all animals have limits and as the adult human it is your responsibility to not push those limits to the breaking point.
Part of my advice then is to be realistic about who your pets are. Train and expect the best possible behavior but be keenly aware of each individuals strengths and weaknesses. I notice for example that while Jenny loves to greet people and enjoys children, she was not raised with small children. I also note that when small children are very squeaky and fast moving, Jenny needs to be able to move away and come back at her own pace. I never require her to stay next to a small child or force her to stand still so that a small child can pet her. The interaction lasts as long as Jenny wants it to and when she moves away, the interaction is over. I also do not leave her unattended with small children. I'm fairly confident that she would never harm a child but I also will not bet her life on what could happen in a fraction of a second if she were hurt or scared.
Gracie on the other hand has the potential to knock a child over or accidentally scratch them from over enthusiastic playing. There is nothing a child has done however, that has made Grace nervous, or that has made her react in a negative way. My nephews have grabbed her, fallen over her, run and played and accidentally they've stepped on each other. English bull terriers have a high tolerance for pain and hard play so while the children are being taught respectful behavior of animals, any accidents they have are safe to have around Gracie as far as a pain threshold goes, i.e. she does not have a sharp reaction to accidentally inflicted discomfort. Of course, she also intentionally crashes off of furniture when she has a sudden need to race around the house and build up speed. It's yin and yang. High threshold for pain goes hand in hand with a lack of overall daintiness, no sense of personal body space, and interestingly a belief that the world is full of potential best friends waiting to be pounced on. Grace does not seem able to process the fact that not all potential friends want to be pounced on, jumped over, or crawled under. I have to restrain her around subdued individuals of all species because her personality can be pretty overwhelming.
When considering adding a new animal member to the family the potentials I've discussed can overwhelm people. Should they get a young animal that can learn "normal' is what happens in that family? Should they get an adult animal who's personality is already a known? I argue that either can work out, this is more of a personal choice that should be guided by an honest appraisal of what the adults in the home are up to.
Adult pets adopted from reputable sources will come with a description of how they interact in particular situations that they have been deliberately exposed to. Their energy level will already be indicated by what has been observed. Their ability to be around and their behavior with other animals will already be noted. An adult animal can be introduced before adoption to other family members including other existing pets.
Young animals have much to learn. They need to learn where/when it is appropriate to relieve themselves; what is and is not a toy they may play with; which surfaces they are allowed on and which they must stay off; what the acceptable level of teeth, nails, and attitude are when playing. If the adults of the family are prepared to take responsibility for training and setting the tone of acceptable behavior for all other parties, then this is an arrangement that can work well. If the adults have little experience with animals then they should be able and planning to pay for training and education to help learn. If lessons are not possible, then adults should be taking books out from the library and reading. Read books and online sources and learn to discern what is good advice from what is bad.
The best advice I can give to potential animal owners is to be prepared for the most likely possibilities that will grow from the choices you make. From how an animal is trained to the genetics they inherit, animals have some predictable possibilities. Be educated and take responsibility for those things which you can, and you will be that much better prepared for when the unpredictable eventually shows up.