I would take the puppy to the vet and see if they can identify the specific breed. If she was a stray, most likely all mutts for the puppies. Any dog can be good with children as long as they are taught to withstand some roughness from humans. Also teach the children to be gentle with any animals.
From her body I want to say pit or boxer. Her body looks a lot like my boxer. Her face looks like a lab.
Really it depends on the dog not the breed. Mutts are usually good dogs and have fewer health problems. The puppy looks like a lab . She looks like a good dog. In the last pic, she's looking at you and not in the bag of food that's right next to her.
It looks like what they call a Heinz 57, so many breeds in the mix that one is not more dominant than another. All dogs are only as good as they are treated. How do you treat the dog? And regardless of breed I would never leave an infant or small child alone with any dog