I would recommend finding the right individual dog rather than getting your heart set on one specific breed and nothing else. In general, and also based on the fact that your most recent try with the pittie did not work out, I think your household might enjoy a mature, fairly mellow, social, and tolerant dog. I can think of many individual dogs I've met who would be wonderful 'family dogs' and they span many breeds. I'd recommend a dog with a good history with children. I have many stories of families with a (lab, GSD, aussie, puggle, chihuahua, weimeraner, [insert breed here]) and kids who are struggling because the dog is nipping kids, or shredding their toys, or knocking them over... The list goes on. Point being, it isn't necessarily a breed thing. A puppy would be really hard, no matter the breed. I've seen many puppies either fearful, overwhelmed, or overwhelming for very active families with young children. It can be done, of course! But it comes with months of interrupted sleep and a lot of training and other work.
I'm thinking of the most family friendly dogs I've come across, like the dogs who have allowed kids to zip around them and literally hang off their necks (never recommended, but I get that it happens)... The ones who come to mind have all been young (6mo - 2yr) shelter dogs who were well matched to that family by that adoption agency.
A good idea might be to look for a retired dog with great home history from a reputable breeder, or visit your local shelter and tell them exactly what kind of dog you're looking for. You would want to bring your whole family for the meet and greet. Look for a very human-social dog who is gentle, confident, and and eager to interact. I've seen dogs who do alright with kids during a greet come back due to lack of interest in the kid or defensive behavior in a home environment. "Alright" as in, the dog in the shelter was fine with the kid, no red flags, took treats... A stark difference from the dogs that I've seen THRIVE in households with kids, the ones who are all over them (in a gentle way) from the moment they meet them. Yes, dogs get to be totally different in a home and a kid-aloof dog can turn out to be a total love bug. But by and large, that first impression between dogs and kids is pretty telling. Yes, dogs are stressed out in the shelter. But the 'bombproof' dogs that do great in homes with children are still very social with people when meeting them.