I was in a rental car and was not asked or offered insurance nor did they check to see if my insurance was valid, a drunk driver hit me with my kids.

Did the other driver have insurance?  If so, then they would be liable if the accident twas the other driver's fault.  Also, did you have your own insurnace?  You probably need to call and get a get free consultation with an attorney.  You would benefit by knowing all your options beforre you proceed with this claim any further.