Got rear ended by someone with shoddy insurance

I got rear-ended by another car. My family was in the car, including my 4-month-old. I got out of the vehicle and politely asked for the license and insurance information. The driver of the offending vehicle was immediately apologetic; however, they tried to downplay the issue and wanted to offer me $10-$200 for the damage, which clearly doesn’t cover anything these days. He spoke in Spanish and told me that he didn’t know any English and requested that I don’t call the police, which, from what I understood, was because of his immigration status.

I told him that I just needed his license and insurance information and offered mine. He gave me the insurance information immediately; however, he wasn’t willing to share his license information. Eventually, after half an hour, I somehow convinced him to get his license information and took photos of the accident.

The other driver was clearly drunk, and I did call 911. However, they told me that since no one was apparently injured and if the car was drivable, I should drive to the police station. I tried to waive a police car passing by, but he just told me to call 911 since it wasn’t his sector. At this point, the other driver started behaving erratically, shuffling through his car, and I felt like it was better to leave the situation since I already got his information. As I got in the car and drove away, this guy followed me very closely up to about three intersections, and then, as I turned right, he turned as well. He eventually gave up following me.

I filed a police report later. I called my insurance company, but they recommended that I contact the party at fault’s insurance. I looked up the insurance company, but based on their Google reviews, it looks like I am not getting anything from them. It seems like it’s a daily occurrence for this company and its clients. Regardless, I plan to call them on Monday when they open.

Now, all that said –

1. How did I handle the situation? What more could I’ve done?

2. Would it have been a good idea to get that $200 as security?

3. What recourse do I have if their insurance isn’t responsive?

Thank you all.