Re the ability to judge a dog's intentions by its body language: veterinarians and their staff do it all the time. I teach the basics to my staff very early in their training and the skill is constantly refined. No reason at all that people who around dogs a lot, including, apparently, OP, cannot skillfully read the dogs' attitude.
Can dogs injure and incapacitate quickly, with one bite? You betcha! A very skilled member of my staff had to have very expensive hand surgery and extensive physical therapy after a single bite that happened so fast we were all stunned. The idea of waiting to be bitten before defending oneself or others from a dog bite, in the professional opinion of this 27-year veteran of veterinary practice, is nothing better than asinine.
We should also consider that if the dog is close enough to bite, the OP's firearm is going to be pointed at rather severe angles, always moving with the target, and the "what is behind the target" concerns, for both misses and over-penetration, become very difficult or impossible to deal with. And most dogs are smaller bodies than humans, so even placing a muzzle against the body wall risks having a projectile exit with significant enough velocity to injure or kill.
It is hard to criticize the OP response to the situation, IMO. He used the gun as a noisemaker rather than an instrument of injury or death, but it was effective. I have little doubt that his own body language played a significant role in redirecting the attacking dogs, but together with the noise from the gun it worked, and I am in favor of what works. Like some of the other posts, I have been under dog attack (outside of the office) in a pack situation, and it is a very fast-developing and highly dynamic situation, very frightening. Dogs are quite intelligent animals and out-thinking 2 or 3 at a time can be very difficult. I would say congratulations to OP are in order for getting himself and his group of vulnerable people, especially the kids, out of a very sticky situation with no injuries to human or dog.