Auto Insurance Claims: what now, chevy caviler, chicago insurance

Question
I live in Nebraska.  Last month my daughter(who is on my Farm Bureau policy) along with another daughter and a nephew took her car(90 Honda Accord)to Chicago for a short trip.  On the way back as they were passing an 85 Chevy Caviler on the interstate a tire blew on the Caviler  sending it into our car's lane.  Her back hit our front and sent her into the ditch.  My nephew was driving.  No citations were given.  We contacted our insurance company when they returned and our insurance office secretary called the other lady's insurance company.  They wouldn't talk to her because the other driver hadn't contacted them.  My insurance company sent they lady involved a letter saying that they were handling a claim in which she was involed (but not claiming libility). We've had some estimates on our car which I think they will total because of the age and miles.

The other driver called my nephew today (as he was on the accident report as the driver)and said she was turning this in to our insurance company.  

When I got home from work today there was a call from an Chicago insurance company on my caller id but no message on my answering machine.  I don't see how we would be liable.  Not only was my daughter not driving but the other lady did not have her car under control. My daughter has been without a car for a month now.  What do I tell these guy when they contact us?  What do I do next?  I don't feel I should have to bite the bullet on this.  

Answer
This sounds like at highway speeds, it could have been much worse.  Try to keep that in mind.

You state that no citations were given but if the facts that you presented to me are on the accident report, then the other company needs to investigate the claim and pay your damages.

Based on the lost facts and all of the witnesses in your car, I doubt that you have to worry about being liable here.
The lady needs to be advised not to contact your family from this point forward.  She's probably a nut.

The fact that your daughter wasn't the driver has no bearing as insurance follows the car, not the driver.  As long as your nephew had permissive use and is not residing in your household as an unlisted driver, there shouldn't be a coverage issue.  If the other carrier is liable anyway, your coverage wouldn't be an issue.

The best thing to do right now is:
Obtain the other driver's insurance info from the police report.
Send a certified letter to her and her insurance company outlining the facts of loss along with the repair estimate for your car.  This will wake her and her insurance company up.  
You'll also want to make sure that your nephew and the passengers are all available to give statements to the insurance investigators from both companies.  Difficulty in obtaining statements is what slows the claims process down more than anything.
If you follow these guidelines, I believe your claim should be settled fast and fairly.  If you are still having trouble, please let me know.

I'd also appreciate your feedback.