My situation although similar is different, my dog now has dog aggression from a terrible incident. She has never and I am sure will never bite a human, my little dog when younger bit my face, and actually bit my daughter so she needed stitches, she got between him and the cat that wanted to eat him, so I didn't blame him, but we worked with him, and now have him at playgrounds and around kids all the time, he was a rescue, but he was young enough that we could reverse it quick. I have had great success with a behaviorist, I had to bring from winnipeg, over 2 hours away, and worth every penny. There are ways to work on it, and work everyday. I agree about tireing the dog, especially working dogs. You should not have to live a life where no one can come over and your kids cannot have friends, that is no good either. There is help out there if you are willing to get it and work at it.
I would always work with a dog as much as possible when the signs start showing. If a dog bites out of aggression unprovoked at a child the situation needs to be looked at with clear eyes. If kids were running and playing and a dog bit out of a prey response, then I think being pts needs to be honestly considered. If a dog bites for a reason, being hurt, provoked, then I feel they should have a chance to be rehabed. But that said I think if someone has seen aggressive signs something has to be done quick and often. Keeping the dog isolated and in turn isolating the whole family will not help, but hurt, and may make the aggression work. As much as I worried about having my dog around other dogs, I had to get the skills to handle it, and do it. There has been one episode where my guard was down and she got at another dog and bit it, drawing blood.. Dealing with this towad humans must be so much harder and scarier.. use the muzzle if that is what makes you calmer, your energy is important. And do the work with a muzzle on. But don't isolate.