If I had spent as much time as you have described trying to put her relationship with your children into perspective (conversations, letters and avoiding her) and asking her to respect your wishes about no contact with them and she STILL went brazenly ahead and met your child at the school, my strategy would not be to act as a nice neighbor to the family and maintain contact.
I would have made it clear to her and any of her family you still speak to that if she took it upon herself to have solo contact with your girls going forward, I would be talking to my local police department to find out about my options.
It reads to me like she has some boundary issues that extend beyond your property line, former babysitter or not. Neighbor or not. An adult with healthy control of their emotions and actions would not ignore you like that or insinuate themselves into your family's life when they weren't wanted.
As for your girls, I thought that the other moms had great suggestions on how to explain the break. When I was a girl, my family had a serious experience with a similar situation. I don't know that describing it would be useful as it was pretty extreme, but the lesson for our family was to err on the side of caution.
I don't know that any of that helps, but I hope that the situation resolves itself and she begins to respect the boundaries you and your husband set.