回複：six year-old boy was pushed down and arm was broken

I think the best way to solve this would be that you talk to the other parents to pursuade them to pay for the medical cost. Going through court would be time consuming and not economically efficient. The lawyer would take 25-40% on whatever damage you can recover. Besides, punitive damage is hard to get.

If you decide to sue under battery, the chances are, the girl would deny her intention, as they normally do, even under oath. She could say it was an accident or it was consented. Then the defendant counsel will move for a demurrer or a summary judgment later and the case would end right there. You won't gain anything on appeal either since it is your burden to prove her intention by preponderance of evidence and based on your saying there is no circumstantial evidence to support that.

The second choice is to sue her under negligence. The jury would evaluate the girl using children standard of care of children with similar age, intellect, and experiences, and her failure to avoid the risk would be a breach of that duty.

Again, find a lawyer and ask for advices. Ask the lawyer if in your state there is any strict liability statute or criminal statute which could allow you to sue the school under negligence per se.

For the parent part, there is no ground that allows you to sue them.