When I was around 10 or so there was a German Shepherd on my road that used to chase me every single day after school. This was some years ago needless to say and back then there weren't really enforced leash laws to speak of. The owner would be there on the porch and lamely call the dog or not call the dog at all. My mother always told me, "just don't show fear and keep your hands at your chest". That's what I did every day, until finally he attacked me, wrapping his jaws sideways around my little hip before his owner called him off. I walked the rest of the way home, bleeding, needing stitches. My mother called the police. The Sheriff came out and without court proceedings, charges, etc, simply SHOT the dog. (As I said, this was a few decades ago).
Around the year 2000 I had adopted a Lhasa Apso who had known issues with children. Apparently he was in a home with kids who tormented him, so it was made clear that he was an adult only dog, but loved adults. Having no kids, I adopted him and tried my best to give him a great home. One day, I leaned down to his face and said something like "What a good boy", when he reached up and bit my nose wide open, requiring over 30 stitches. I still have the ugly scar.
You may think I'm proving the point to put down vicious dogs, but it's the opposite. I truly do not believe that either of those born-innocent dogs deserved to die. Even with a scar around my hip and one on my face, I still believe this. The dogs were not brought up right. It was the owners who behaved wrongly, and raised innocent dogs to know no boundaries, not calling them off or letting their kids torment the dog. This is the OWNER'S fault, not the dogs. There are no bad dogs, only bad owners!!
I am in total agreement that this women should not have come to this event if she knew the dog was nervous around kids. But the OP did not say that. She said the women apologized and said her dog was nervous around the kids. Maybe the women was just discovering this. Maybe she went home and said to her husband, "We need to bring Fido to some serious training because he was nervous around kids today". We are assuming she's some wretch like the neighbor that repeatedly allowed her dog to harass me, but we don't know if this is the case.
Dogs can be re-trained. They do NOT need to be put down so easily. Maybe if we put our efforts and opinions into re-training the dog owners, we could save a few dogs who deserve responsible owners. If I found out my kid lunged at another kid at school, should I assume he's a danger and kill him? Of course not!
