Perhaps I am a bit pessimistic, but I don't think that you can change an experienced teacher who is so set in her ways. I would focus on insulating your DD from emotional harm so she takes the situation in stride. Help DD to focus on the math but learn to follow the teacher's requirements to the extent possible without undue stress. Give her permission to get a bad grade if she should inadverdently violate one of these requirements. The fact that this teacher will be teaching her for several years is a cause for concern if your DD is unable to adjust this year so a change in school may be necessary next year.

My children has had rigid teachers over the years but your teacher sounds a bit further out there. On the positive side, some of these rigid teachers have been instrumental/helpful in my kids learning to follow directions, showing their work and otherwise acquiring those skills/practices required in middle school and beyond.