I used to be a bodily injury automobile insurance claims adjuster for CSAA in San Francisco back in the mid-1990s. My experience is based on California law, so YMMV.
As an insured, you actually have more power and control over this than you might think. I would definitely file a claim with your insurance and let the adjuster look at your car. I would also try to get a repair estimate from a couple of good shops to use as ammunition. Since the other driver is at fault, your insurance company is going to pay for the repairs and subrogate against the other insurance company to recover their costs. In this situation, they don't have as much incentive to low-ball you on the repairs.
If your wife is feeling any ill effects whatsoever, it makes sense to see a doctor as soon as possible, both for medical reasons and for any bodily injury claim you might decide to make. During all of this, if you feel your insurance company is "screwing you over", you can escalate it to a supervisor and start talking about "unfair claims practices". That usually gets their attention pretty quickly. Writing an actual letter or two to your claims department is also a good idea. Writing to your state insurance commissioner is also helpful.
At any rate, being reasonable, but firm, with good documentation of things like repair costs and appraisal values gives you a much better chance of a good result.
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@lolachampcar It really sucks what happened to your wife and your Model S, so I totally sympathize with you. That said, I would at least file a claim with your insurance company before you consider simply selling the car "as is" and take a huge financial hit in the process. Worst case scenario, you should be able to cash out your claim (where they pay you for the estimated repair costs, after a shop had gone through the adjustment process with State Farm). You want to start out with a repair estimate from a shop you trust, and make State Farm go down from there. Maybe your local Tesla SC can give you some shop recommendations.
It seems to me that if you sell the car "as is" simply to avoid the hassles of a repair, you are going to take a substantial hit on the actual sale value of the car, plus you are going to take the sales tax and registration hit when you buy a new Model S. Someone who buys your current car is not going to be eligible for the $7500 Federal tax credit either (although you would get it again for the replacement Model S).