The only issues you will have will be if your uninsured coverage exceeds your medical bills. At that point you can sue her for the difference. But even if you wi. The likelyhood of collecting is very low. She can just file bankruptcy.
You pay insurance to take care of these things. Let them do the dirty work. You do not need to sue her, you pay insurance premiums so your insurance company can pay their army of lawyers to get what your insurance company needs to take care of you.
You also got it backward- there is likely a lawsuit coming if his medical bills exceed the coverage limits, not the other way around, as you stated.
An insurance policy is nothing more than a retainer for financial and legal services- that's what you pay for, let them earn it.