If the babysitter had wanted to respond in a way that would have helped her situation, she could have expressed gladness that DD was doing well, sadness she wouldn't see her again, promises to think of their time together fondly and hope that if OP changed her mind or needed anything in the future, OP could let her know. Then she should have wished OP and DD the best and been done.
What she did is shoot herself in the foot.
I was sympathetic to the babysitter in the beginning, but now, I wouldn't respond at all. You may get a few more emails, but I doubt she will show up at your house.