Your insurance company isn't going to do crap for you unless you have comp/collision coverage and you're having your insurance company repair your car, pay the deductible then after everything is settled in or out of court, your insurance company gets their money and your deductible is refunded.. Though, that's an IF..
I'd suggest getting copy of the police report and see exactly how the officer wrote up the details of the accident, that will probably give you a better indication of how the insurance companies will rule fault. Did your wife hit the other car directly in the rear or did she hit a rear side corner? If the person hadn't fully returned to the lane your wife was in and it was even a slight side swipe that should definitely put the other person at fault because they returned to the lane before it was safe to do so.
My son was involved in an accident about a year ago where a lady cut into his lane, but tried to say instead that my son cut into her, so there were conflicting stories. I went to the police station and got a copy of the police report and on the report the policeman stated that the damage indicated the lady was the one who cut my son off then continued to drive into his lane causing even more damage to my car. The insurance company ruled it her fault, but then I find out she didn't have insurance as required by Kentucky state law, so I had to get the county attorney's office to file charges having her charged with no insurance and get it in court so I could receive restitution for the damages.
update: legally we have no grounds for a claim against anyone.
FordMan: it was slight a off center contact point...still mostly rear.
next is what to do...
owning 3 cars, we dont NEED to repair or replace this one right away. IF i made a claim(i do not wish to), the car WILL be totaled(first repair estimate $6k) and kelley blue book shows a private seller value of the $3k range. however, there are only 2 like cars in my area for sale, both over $4k.
so what's a fair price to sell the car whole for? i can't see myself letting this drive train gem go for peanuts! it has a perfect engine/tranny, custom wheels, almost new tires, super clean interior, and ice cold air!
If the car still runs and drives good and the no AC damage/no radiator damage someone may pay half of blue book and spend $300-400 at a You-pull yard and get it fixed as good as before the accident.
The cracked windshield might be an issue- did the hood shift backwards and crack it? or the passenger air bag? or is it possible that the frame twisted a bit and if so, a new windshield wouldn't fit/seal properly.
Maybe you can find a similar car with blown engine/tranny and swap your drivetrain into that body.
One time in a snowstorm (for those of you in FL, that's when white stuff flies from the sky) a car in front of me lost control and spun out. In order to avoid crashing the car, I swerved and wound up scraping the guardrail.
Even though I NEVER TOUCHED the other car, he was found at fault and had to pay for my repairs.
Make sure your police report contains the WHOLE story, not just "I hit the car in front of me". Include ALL details of relevant events prior to the accident. It might take some appealing, but (in my experience) the whole story will get told and the responsible party will be held responsible.
In another case, I was driving a classic car and the car was totaled by an idiot. Not only did he (his insurance) have to buy a similar car, but they paid for the sales tax, the contents of the totaled vehicle, and even transporting the car from another area of the country. Yes it took a lot of fighting, but just remember that it is the guilty party's responsibility to "Make the victim whole".
Have you talked to your insurance agent? In most areas the car that rear ended the front car is usually responsible, but as I said if the other driver returned to the lane your wife was driving in before it was considered legally safe the other driver should be held responsible. That's why I suggest getting a copy of the accident report and also turn over a copy to your insurance agent for their opinion before doing anything at all to the car yourself.