I think there is generally a bias in the school system against parents accelerating kids or early entrance to kindergarten, and the teacher is annoyed. She is looking for any fault in your DD to prove her theory is correct, rather than trying to help her succeed. Personally, I think it is probably more harmful than beneficial for her to be in a setting like that where she is not supported by the teacher. If there is any way you can get her out of that school, go for it.
Here, there is an option for early entrance to kindergarten, but only for kids born before the end of the calendar year (fall birthdays). We have a Sept. 1st cut-off.