Most dogs will change, but I would be lying if I said all of them do. Like I said, I have dealt with many pit bulls at a rescue, and the ones that show even a little bit of jumpiness around children are not allowed to be adopted by families with them.
Here’s my problem with this (and please don’t take this as me coming off rude or mean), I would never risk a dog that I don’t feel safe to have around children, around children. Especially my own. This is for two reasons. First, it is scary to think that a loving family dog could accidently severely hurt someone in your home. You don’t want that risk or problem. Second, it is unfair to the dog, because if something were to happen, he would get blamed and probably put down. Then there would be another news report about an aggressive pit bull.
If the dog only growls around children, I would definately think about rehoming him with someone without children who is experienced with abused or rehabilitated pit bulls. That way you can avoid any problems, and most likely save a dog’s future.
This is likely not the dogs fault and by no fault of your own. So don’t feel bad for this happening. Sounds like the previous owners were abusive (although this is just speculation on my part). If you still want to work with him though, definately seek professional help for him and definately monitor him at all times with your children. Most dogs who do attack, give plenty of warnings way ahead of time.
Good luck with your poor baby. Hopefully someone else can give you better news than me.