Can somone explain the auto insurance process after accident pls?

My truck was totaled recently, husband was driving, we were stationary in a left turn lane at an intersection when a vehicle rolled the stop sign causing a vehical that was oncoming traffic to us to swerve and hit us head on going about 70mph. That vehicle that hit us was demolished and has accepted some liability, the one who rolled the sign is denying liability and refusing to talk to insurance.

I was airlifted to the closest trauma center, lost consciousness during the accident amd likely have tbi, def a bad concussion at the least. Tons of soft tissue injury/torn things, abrasions. Honestly feel lucky to be alive, had I been in my little car I wouldn't be. My husband has back injury, like bulged or compressed things and arm injury. I was sent by the trauma center to a brain injury place and have appointments to begin physical therapy.

So now I am not understanding the process of what happens now?? Do we end up suing the one who caused the accident that isnt cooperating with insurance?? She was given a citation at the scene for running the stop sign but Im sure she will fight it in court. Id like to go to the court date, am I allowed to do that? Or can I talk to the prosecutor about it prior or anything? Id really like this woman to pay, she made zero attempt to stop and has really ruined 3 lives at the moment, ours and the woman's who hit us.

I was told by my insurance company that the driver who actually hit us has a "substantial" policy so I feel we will be covered there. The policy appears to be attached to a ranch. They are only saying they are partially liable tho but at least working with their insurance.

How do things progress in situations like this? Is there a chance that the evasive driver will cave and admitt liability? Is it worth me attending the court date for the failure to stop citation? Thanks for any info!