Head on accident

I was involved in a head on that was the other drivers fault: I was driving north they were coming south. They lost control of their vehicle on slick roads and crossed the center line in front of me where hit them in the door. The other vehicles passenger was killed, myself and my passenger were seriously hurt. My injuries include a broken scapula, a compression fracture on my L2 vertebrae, fractured elbow,sprained ankle, among other soft tissue tears and bruises. The other drivers total coverage is $100,000 for the total accident. Their insurer admitted liability(as the case is pretty cut and dry, even in the newspaper press releases and TV news stories) and says there is no way their insurance was enough to cover all damages, physical as well as property. They are going to fax a declaration page over to my insurance, so that we can open the underinsured part of my policy.My uninsured/underinsured is $100,000 per person with a total of $300,000. Since this was such a serious accident will my insurance company just cut a check for the Limits to get this out of their hair? This has put my wife and I in a serious bind, as I am now laid up and we have no income for car payments, mortgage payments and such. Thanks in advance. M