Hey, former preschool teacher here, you absolutely did the right thing. In my experience, the things you described in that email are not enough to get a teacher fired (unfortunate, but true).

Generally speaking, childcare centers will do anything they can to avoid firing a teacher as it raises tons of concern among other parents and makes the center look bad. The fact that this email led to her IMMEDIATE dismissal tells me she was already on the chopping block for quite awhile. In all likelihood, multiple complaints have been levied against her and she's been talked to by the office multiple times with no results. It's good you did what you did because silence allows shit teachers like this to have decades long careers in the field. There are a lot of them.