I'm convinced the only people who know how to deal with insurance companies are insurance companies. If you turn it over to yours, they should know the right way to say "come back with a court order". Of course, we're all afraid of our premiums going through the roof, so no one wants to use their insurance for what it's for.

Did you get the other drivers insurance information and/or file a police report? In a lot of jurisdictions you can file a police report online and never have to talk to anyone.