Sorry to hear about your accident.
I'm not an expert on auto insurance, but I have had to file more than one claim in my driving career (stupid Northeast drivers

). I've never had to deal with an uninsured motorist, though.
Subrogation basically means your insurance company tries to get money out of her insurance company. However, if her insurance has lapsed, that won't be an option. If she has new insurance, your insurance company can go after her new insurance company. If not, probably your only option is to sue the other driver, since you don't have uninsured motorist coverage.
She should already have been ticketed or something for driving without insurance (if she didn't have new insurance). I'm pretty sure most states require a certain minimum level of insurance.
Another thing... Make sure
your insurance coverage isn't jeopardized. A friend of mine got dropped by her insurance company because she had three not-at-fault accidents in two years (in one case, someone hit her PARKED car that she wasn't even in at the time).
Good luck