I'm really sorry you had to go through this, as A responsible dog owner and longtime dog walker, I've been through a situation like this many times. People should not let their dogs off the lead in a public place, ever. In a enclosed dog park, you know what you're in for, your chose to go there, otherwise, it is against the law for dogs to be off the lead.
"Oh he's friendly" "Oh he doesn't bite" "Oh he's just excited"... You know what, I love dogs, but I hate owners like this. And yes, the dog may be friendly and typically doesn't bite and maybe excited but that doesn't mean that there won't be an accident, someone especially a small child won't get knocked over or accidentally bitten, I say accidentally, because it can happen, just the edge of the dogs tooth as his mouth is open as he's panting can smash against a child's skin and tear, I know, cuz I've seen it happen.
It wasn't a "bite", but it was a dog mouth/teeth causing lacerating damage to human skin.
I began carrying a high-powered and brightly neon colored water gun. (Think super soaker.) The kind you can pump up with air. Brightly colored because you don't want anyone to think that you're actually carrying a weapon. Not gigantic, but enough that it's got some oomph to it. I hang it off my belt, and when I go for a walk It's pumped and ready to go.
I also carry a large walking stick that is very solid.
100% I agree with you that this other dog owner was in the wrong. I don't blame the dog so much, dogs are just doing what they do, but the dog should have been on a leash and under control. Your dog or your children or both could have been injured, intentionally, or through play. Doesn't matter.
Most dog owners are responsible, law-abiding, poop picking, leash using, and careful.
The irresponsible dog owners should be neutered.