
It's really impossible to "diagnose" behaviour problems, especially second or third-hand. Not sure what you mean by "attack" - dogs that attack eventually end up in dog fights and you have not said that has happened.
One of my dogs is fearful, he's lovely and affectionate and more than any other dog I've owned always wants to do the right thing. He is good with other dogs. However, if they frighten him he will growl at them - anyone that knows dogs can tell it's a bluff. Once the other dog backs off he's absolutely fine and is content with some polite sniffing. He also has a "time limit" on sniffing - if another dog lingers too long he tells it off.
He is often given to growling if he is comfortable and he needs to be moved. It's not a growl per se; he's just grumbling and showing his annoyance at being shifted. Being shifted on the duvet was a big one for him; but as I shifted him I'd say "move over" ... and now all I have to do is give him the command. If he really has a hissy fit type growl, the next second he comes back to me, tucks his head under, and presses against me. It's as if he's shocked himself and needs reassurance everything is still okay. I have never had any concern that he would actually do anything more than growl/grumble. Even with other dogs, when a large boisterous dog ignored being scolded what my dog did was roll on his back in submission.
In terms of growling at children, for the nine-year old it would be ideal if she could take charge of more things for the dog - such as feeding, teaching him some commands or tricks, etc. Dogs and one year old children should not be left alone together, of course, neither should they be put in the position where the child can annoy the dog whilst they are eating or sleeping. Many dogs grumble when they are disturbed while they are sleeping.