Sorry the day didn't go smoother.
I do like the part where the principal actually came. And then even more the part where her own teacher and the principal ignored her, while she was able to blow off steam at a third party. That actually sounds ideal. It's great she saw that if she throws a fit it will be taken seriously but also great that after acknowledging it they moved on with their day (and didn't reward her either by calling her dad to come get her).
I wonder what your DD would suggest for what the teacher should do with her rather than a time-out type chair, for when she is disruptive?
Seems like the teacher and principal handled the first day well (well minus the naughty chair idea). It does seem good that the teacher has lots of experience, probably has seen various other kids with behavioral issues over the years. Hopefully once they get over the initial shock of having a difficult student maybe they will have patience and see it as a challenge.
Great that your DD basically enjoyed her first day. The desire to be allowed to attend could be a great motivator for her to learn appropriate ways to express herself.
