This is a simplified/fictionalized event to help me understand the law/my rights. If jurisdiction matters, I am in New Zealand.
I have a vehicle which has sentimental value to me in excess of its insured/book value. My car is rear ended and the other party is at fault. The value of repairs is a about the value of the vehicle. The other parties insurer - who I am dealing with directly - wants to pay the book value of the vehicle (and take possession of the vehicle and write it off).
I expect that writing the vehicle off is advantageous to the insurer as they will be able to recoup some small part of the value by selling the car as a write off.
Am I entitled to get the vehicle repaired and require the other party/their insurer to pay the costs of the repair or can the insurer force me to accept market value and take my vehicle? What law/type of law covers this kind of issue? (I suspect this is tort law but have not been able to find any concrete information on this)