Hi, I am by no means an expert. Our male boxer is only 8 months old but he has grown alot recently and I had worried a little about him playing with my girls, (ages 3 & 4) but we just let him feel like part of the family. We do set limits on things, like he can't get on the furniture anymore (we shouldn't have started it when he was small). But he got his own beds when we quit allowing him on the furniture ( one bed in the den and one in our bedroom). Also make sure your puppy has its own toys to play with and never allow him/her to play with the children's toys. Cooper already knows the difference in his toys and their toys. Also, as tempting as it is, cause you want to spoil them, don't feed them from your plate when they beg for food. Keep them away when the children are eating until they understand that they can't eat from people, they must eat from their own bowl. I do allow my children to give him doggie treats for "sitting" and "shaking", he caught on very quickly. And he takes the treats very tenderly from their hands. I don't know if we just got lucky and got a more calm puppy or if we properly trained him from early on. ALWAYS be where you can monitor the dog and the children together. I wouldn't feel comfortable introducing an older dog into our home at my daughters ages. That is just me though, I have never experienced that so I can't really say.
Hope some of this helps!