Am I obligated to bear the full cost of repairing the car, and can I guarantee the car without my knowledge, given the other party's refusal to reconcile?

If the driver of a car makes a mistake and causes a loss, the loss falls on him alone, even if he was driving it at the request of another person, or if his guide made a mistake. The crime obligates its direct perpetrator, and ignorance of the consequences is not an excuse that removes liability. As stated in "Nayl al-Ma'arib," whoever orders another to commit an act that leads to destruction is not liable for it. And as mentioned in "Al-Ashbah wal-Nadha'ir" by Al-Suyuti, ignorance and forgetfulness remove sin, but not the ruling or liability if the act involves destruction. Although chivalry dictates that the one for whose benefit the car was driven should bear the costs of the mistake if the driver was not negligent, this is not a legal obligation.