I added a couple addtl points above by edit because I hit reply before I was done.
You're quite welcome, and yes, it is a very frustrating process.
You don't NEED to use the other insurance company. If you have collision coverage you can choose to go through your own if you prefer, but, they will withhold your deductible until the other company tells your company they accept fault (doesn't matter you are told they accept fault, it has to go between the companies.) Depending how it all goes that is a consideration.
Not sure of your living situation, or where the car is, BUT, if possible you should consider whether you need to try to regain/secure possession of it if you expect to be arguing value for any length of time. Once the insurance decides it's total loss, if they continue to have to pay storage charges on it because you delay the process they may try to offset your recovery for those expenses. If you can store it yourself then you can fight as long as you want and they lose that leverage.
Typically you're going to get stuck in the middle on values. You'll find high end comps. They'll go for what's cheap. Pull out nadaguides.com, grab some issues of old cars price guides and the like. Get some sale listing from hemmings - cars sold by businesses may show sold on their websites with a price, especially consignment ones. Private seller if you notice a car was there last month and now gone may be happy to tell you what their car sold for or even write an email stating it to help a fellow enthusiast out. Look for recent results if any cars went through mecum or barret jackson.
They may have said they thought yours were too high, but, make them say why and how.
Your state govt will have an insurance commisioner, and it can be buried in a weird sounding department. (Here in Georgia the title is the Office Of Insurance and Safety Fire Commissioner, weird right?) Anyways, most states have penalties insurers are subject to if they done process and offer to settle claims in good faith, and, when you invoke the language in the right way - explaining why what they do is bad faith - typically results suddenly change. This is why you need to get their actual basis for their valuations. Did they find other cars they thought were comperable? Have them send the data on it. Did they discount something working down from the comps you sent? What?
Remember - the person you're talking to is basically just doing their job. If you find yourself getting emotional or voice rising, feel free to take a second, stop what you're saying, and tell them you're sorry if you come across angry, it's not them, you're just frustrated by what happened and the process. More flies with honey and all that. Their job is to try to settle claims for as little as they can.
