Auto Insurance Claims: property damage liability, uninsured motorist coverage, uninsured motorists

Question
My wife was involved in accident where the other driver is at fault.  My wife's car was considered totaled as the repair costs exceed the value of the vehicle.  They estimated that the vehicle is worth $11,000, but the other person is only insured for $5000 max for property damage.  I do have uninsured motorists property damage liability coverage up to $3500 as I do not have collision coverage on my wife's car.  Could I file a claim with my insurance co. to recoup another $3500 and then sue the other driver for the remaining amount of $2500 that is not covered?  

Answer
If your state allows underinsured to be covered as part of your uninsured motorist coverage, then this sounds like a good plan.
Honestly, I'm quite surprised to learn of these extremely low limits.  What state do you live in?  
Most states have am minimum liability and uninsured limit closer to $25,000.