Who to file suit against to recover damages regarding an accident?

Question Details: I was driving on a main roadway, I then turned into a right turn lane and right before making the turn a person next to slammed over into my vehicle. I obtained an estimate as requested by the at-fault partiesat-fault driver was also cited by the police insurance company. They didn't like the estimate saying the damages don't line up, so they sent out an investigator to measure both vehicles then came back saying they would only accept the damages to my fender. I sent them a time stamped video of me leaving work minutes prior to the accident for them to review. They have now sent me a revised estimate from their preferred body shop which was originally quoted and are now offering me considerable less than the amount of the repair cost. What should I do? Do I have to accept this low offer? Do I even have a chance in court on my own if I have witnesses and a time stamped video proof showing vehicle condition minutes before their insured slammed into me?

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