Some children of eight or nine grasp the principles the moment they are exposed to them, and can go right to work; having no preconceptions they catch on a lot quicker than adults sometimes. But I think three is a bit too young for the insight into cause and effect that clicker training takes. By all means she can click her stuffed animals or pretend animals; but I'd suggest that with the cat and the dog she be allowed to click and give treats, three or four treats per animal, once a day, say. That will be clicker training, as far as she is concerned; she'll understand more about it as she gets older. Meanwhile the dog will incidentally learn to sit and hope for treats from her, and the cat might learn the same.
Someone recently wrote to me for advice on a difficult situation developing between her dog and her baby. When such a problem arises, I think you need to teach the baby that he may NOT sit on the dog, pull ears, bother the dog when it's lying down, hit it with toys, and so on. You can't do this with punishment, babies can't learn that way; but you can do it. The dog needs to learn to get up and leave if bothered; but the baby needs to experience being removed, gently but firmly, from the dog, long BEFORE the dog has become irritated to the point of growling.
Random or variable reinforcement is a useful procedure in making a given behavior resistant to extinction, for example in the shaping process, when one wants to raise criteria. To go from reinforcing every response to selectively reinforcing stronger responses you need to develop enough resistance to extinction so that the animal neither changes the behavior instantly upon going unreinforced once or twice, nor quits altogether. Resistance to extinction is also important in maintaining long duration behaviors, as in searches, field trialing, and so on; and can be developed gradually. Bob and Marian Bailey might consider this simply another example of a shaping schedule.
People call many behaviors aggression, and talk about "treating" aggression as if it were a medical entity, like a staph infection. It's as if any display of symptoms confirms the existence of a full-blown case for which known treatments exist.