Auto accident - parent's liability for a minor

What is the name of your state?
Texas

I was hit by 17 year old who lost control of his pickup truck. My vehicle was totaled; the bone in my upper arm was shattered. The young man was ticketed for traveling at an unsafe speed.

The property damage portion of the claim is on the verge of being settled.

As for my personal injury, the claims adjuster has twice implied (but has not come right out and stated) that the kid only has minimum liability coverage--in Texas, that would be 20K per person and 40K per accident and that I may have to make claim under my own underinsured motorist insurance. There was a third vehicle involved; the driver of that vehicle was slightly injured.

My question: To what degree is a parent responsible for a minor in a case like this? Is there a way to find out what coverage levels the insured actually has before I submit a demand letter and/or without hiring an attorney?

Thanks,

dontex