my dd had a lawyer who didn't know her court date was a trial. She was not prepared at all. The lawyer didn't?

Almost certainly not. You are describing a civil case. In civil cases, parties are generally stuck with the incompetence of their lawyers. You can appeal, but you will not be successful unless you have a sound legal basis for appeal. I can firmly state that the argument your lawyer made would inspire a laugh from most judges.

You might consider suing your lawyer for malpractice. However, it doesn't sound like the money involved is enough to justify hiring a lawyer, and most lawyers won't take such a small case on a contingency basis. Also, in order to prevail in a malpractice case, you must show that a competent lawyer would have obtained a better result. I don't know enough about the case to have an opinion, but from your description, that might be difficult to prove.

You might also file a complaint against your attorney with the bar disciplinary board of your jurisdiction. They generally don't consider allegations of incompetence, but your description indicates that the lawyer's incompetence was extreme. This won't reverse the judgment, but at least you might save others from the same experience.

How do you know your "dd"s lawyer did not know the trial date was a trial date? What witnesses or evidence for "your dd" that was not presented would have made a difference in the outcome?

Is the $12,000 the judgment or the lawyer's bill? You can argue the lawyer's bill if you want, but the judgment does not appear unreasonable for damage by a motor vehicle to a barn (and fence, land leading up to the barn?).

And is 18 not the age of majority? "Your dd" does not know enough to drive slowly and carefully on an icy road because she is 19?

Perhaps you failed to educate "your dd" about icy road driving, not to mention driving too fast, or negligently, for the road conditions.

Appellate procedure varies a good deal from state to state. Can't say what yours is, but your Notice of Appeal must be filed on time. If it's not, then no appeal.

You probably won't be able to get a rehearing, but you can file a grievance with your state's Bar association.

yes, as long as the judge approves it