Daughter Got Hit By A Car

Long story short. My daughter and I were riding our bikes. In our neighborhood. We are located in Washington state. I had just stopped in the right lane at a stop sign, she was slightly behind me on my left. She was just about to stop when a car was turning left onto the street we were on and struck her. He cut the corner pretty drastically. She got thrown about 8ft. I picked up my daughter and made sure she was OK. At the same time he tried talking to me and I told him I didn't want anything to do with him. I called my wife, our house is just a couple cul-de-sacs away, to come take her to the ER. I got a picture of the drivers license and SUV were he had struck her. He had moved both bikes away from is car, but you could still see how he cut the corner. There was a witness, I walked up to next and got their info and he said he had saw everything and was willing to give a statement. I wanted to get to my daughter and while I was talking to the witness the driver left. Once I got the witness's info I also left to go to the hospital. She is banged up pretty good but no serious injuries.
I did file a police report at the hospital and they got his insurance info, they said they would be issuing a citation. To my question. Do I try and turn it over to my medical insurance, try and work with his insurance, or do I get a lawyer? I'm not looking for a payout just them to cover medical and possibly her bike and helmet. I absolutely hate insurance companies and don't want to say the wrong thing to were they don't want to cover it. I don't even know if he filed a claim with his insurance yet. "Location: Washington state" Thanks in advance