Same way you sue anyone - go to small claims court, get the judgement. How do you COLLECT? Well, that's another story.
They won't have to pay you "the extra" for the extra insurance you purchased (which isn't actually insurance - it's a "damage waiver").
If you paid a $500 deductible, that means your insurance company paid the rest. That means THEY are probably trying to go after this guy to collect the money. In accordance with your policy terms and conditions, they get first dibs on any money recovered . . .and they WILL TRY to recover your deductible.
Subrogation can take anywhere from six months to two years.
Call your adjuster, and ask if this claim has been moved to the subrogation department. Get the subro adjuster's name and extension, and call them once a month to get updated status on the subrogation process.
They'll have more luck collecting than you will - they're the professionals.
Regarding the uninsured/underinsured motorist coverage - the straight UM/UIM coverage is for BODILY INJURY ONLY. You need uninsured motorist property damage to collect for damages to your car. This coverage is only offered (available) in some states. So don't worry too much about the above post saying you should have purchased it.
agent, 21+ years