Car accident, wait online

I was involved in a car accident last year. We (me and four other authorized co-drivers) rented a car from Hertz. It was raining very hard and the car lost control when I drive the car. Five of us were injured and sent to the hospital. There was no other car involved. The rented car was totally damaged. We lost conscious temporarily (about ten minutes) and had light head concussions and some bruise (no any hard injuries such as bone broken). The next day (after overnight observation), we were released from the emergency care.

One of the passengers sued me for more 250K. We purchased all the rental insurance, including car lost and damage, personal injury ($250 for ambulance, $ 2,500for medical expense), and liabilities up to $1,000K

The worst thing is that Hertz Company, my first liability provider, rejected to pay the liability. The Hertz Company explained the rental liability is for the third party liability and the authorized drivers were not covered by this policy. However, my own car insurance (second liability provider) can only provide up to $50K for PIP, which can not cover the claim if Hertz Company, my first liability provider, rejected to pay the liability. My own car insurance company is ready to pay the $50K PIP for me, and want to settle the case (Allocate the whole $50K among four passengers, and all the passengers agreed not to sue me and my car insurance company anymore). However, one of the passengers, who sued me $250K, rejected this settlement. I’d like to ask several questions, please help.

1) Hertz Company rejected to pay the liability. Should the Hertz Company legally be liable to pay the liability?
2) The lawyer designed by my own car insurance company said Hertz Company should pay. Shall I sue the Hertz Company if Hertz Company rejected to pay the liability?
3) If I need to sue the Hertz Company, shall I use the lawyer designed by my own car insurance company or I need to hire other lawyers?
4) Will the lawyer designed by my own car insurance company really protect me and finally get me out of the trouble?
5) What shall I do if finally what is available for me is the only $50K (I did not have any money)?