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I would suggest getting multiple estimates from an independent appraiser. There are companies that can calculate your diminished value based on the damages. Then go to the dealership as well to get a second opinion. Your demand should be based on those numbers.
Yes, it would be the at fault's insurance. I would try the dealer first and see if that works but they will challenge it as biased so if it is a high enough number then it may be worth it to you.
Let me know if you have any additional questions.