What are the chances that the driver at fault will pay us the settlement amount?

I was in a car accident about a month ago, and the other driver was at fault. He was cited and after talking to the driver, his insurance company accepted that he was at fault. They've already paid or my car to be fixed, and a rental car for me while it was being repaired. The car was about $3,600 to repair and I have a little over $3,000 in medical bills (I had whiplash, a concussion, and big scrapes and bruises on my forehead). Also my 3 yr old son was in the car but he was not hurt. My lawyer requested $15,000 in the demand letter (all for me because my son was fine) After 2 weeks of hearing nothing they finally responded to my lawyer asking for my AND my son's social security numbers. Do you think they will give us the full $15,000? and since they asked for information about my son are they going to give him something as well?