Can some experts please guide?

My car was waiting in traffic when another car shunted me from behind. My car was propelled forward hitting another car as well. In total three cars were involved and my car is badly damaged in the rear and a relatively lesser damage on the front. I reported this to my insurer and they processed my claim (under my fully comp cover stating that they would recover costs from the third party), but a few days later the third party claims management company called saying that their client (the person who hit my car on the rear) had instructed to deal with my claim. As I had to pay an excess on my insurance and also bear the risk of losing my no claims discount (if all costs were not recovered) I decided to switch and initiated claim on the third party direct though their claim management company. The third party insurance company have now declared the vehicle as a total loss and have offered cash settlement, less the salvage value of the car. I do not agree either to the total value offered nor their salvage value as both are not fair (I have some evidence to back this). Some of the salvage companies that I have contacted are only offering far less for my car. The questions

1. I do not want the wrecked car if cannot be repaired. I want the third party insurance company to keep the wreck and give me a full cash settlement. Is this my right and can I insist so? At the moment the third party claims management company says it will be my responsibility to deal with the salvage (Which I am OK as long as they use the price my salvage company is offering in the settlement)

2. What happens if I cannot reach an agreement with the third-party on both the value of the car and the value of the salvage? Can I complain to the Financial Ombudsman?