Put it this way. I looked at your post over and over again but from what you described, it is really hard to tell what you can do legally. There is not solid proof what the teacher did wrong. She or he did give you until that monday to provide evidence but you were late by two days. Even if you did bring proof to school on Monday, it may not change the result anyway. The teacher is free to believe either side.
Moreover, the jacket is two years old and your daughter will outgrow it pretty soon. I thought about whether you may sue the other girl for conversion but it is hardly to believe anyone would go to court for $10. Even if you won, so what, the court can award you the jacket but it would not compensate your daughter's feelings.
Although you do have my sympathies, the only thing I can tell you is, buy her a new jacket.
