As you are (presumably) not a lawyer, the only thing you can do is help her hire one. This is not a DIY project for either of you.

I don't see how this is bad faith. They denied your claim. That happens all the time. So now you can sue them.

I am not licensed in Illinois, but I have no question that a judge would rule that you are 1/2 responsible for the orthodontic work.

Charges are not magically dismissed. These are serious charges and you need to be represented by an attorney.

A court order is not an invitation. If you don't show up, you can and likely will be arrested. You may need to retain your own lawyer.

This is a Q&A forum. You have not asked a question. If the question is what you can do, the answer is not much, as you are not the client. It is up...

This is a Q&A forum, and you have not asked a question. If you had a lawyer, ask them. If you didn't, get one ASAP.

You could theoretically sue in small claims court, but you have zero proof to substantiate your claim. I don't think a judge will rule in your favor.

You are assuming the hospital is right, and the cardiologist is wrong. Even if that is the case, you don't seem to have been harmed by this.

While unknowingly, what you are doing is breaking the law. You are practicing law without a license, which is a crime in every state I am aware of.