Our dog has been around my child since birth and cats (acquired recently) have an area that is "their house" but have free range of our home. Our dog is part of every part of our every day living: walks, park, chores and is an inside dog. She has been strictly trained and is seven years old (so she's a "good" and mellow mutt-dog). The kids feed and water her, walk her and love on her. They have claim to her and take care of her.
I would suggest not keeping the pets away and just dealing with it as it comes. Anything I keep away becomes sought after. The cats, for example, keep themselves away (strays who were not used to humans)...so they are more sought after than the dog. We play with the dog, throwing sticks or balls, petting, lots of positive reenforcement, etc. Their "job" is to help take care of the pets. The pets "love" them so they have to show the pets that they "love" them in return. I show them how to practice commands like "sit, stay, dog out, roll over, heel, come-come, drop it, etc." Thus, they are the alpha, but have a really close relationship with our animal-family-member. It's involvement + love + part of the family + discipline (teaching them the language of animals).
BTW there have been a few times when my daughter has been too rough with an animal. Not only has the animal let her know their displeasure, but so have I. Not necessarily in the form of time-out, alone. I have really shown them, through my face and voice (and the dog's face and "voice"/baring of teeth) how serious it is. It is the same as our wood stove: Some things are a no and some things are a NO! (you're in danger/your in danger of hurting someone else! Stop NOW!) They are both incredible with animals now.