There are too many unknowns to your questions. The best thing to do is to speak with a personal injury attorney who could help your brother navigate through these and other questions to determine the best course of action. RCW 46.61.145 governs rear end collisions. Furthermore, in the event the other driver doesn't have insurance, if your brother has UM/UIM coverage, it would be covered under that coverage.
Did your health insurance company pay for your medical expenses? If you answered, "yes," your health insurance has right to be reimbursed. You should speak with a personal injury attorney who could review your case and go over your options in details.
People involved in auto accidents have up to certain days to file a police report. Do it immediately and have her open a claim with the insurance company. Also, if your mom is injured, your mom should seek medical attention. Also, she should speak with a personal injury attorney. Insurance companies tend to play games and if she doesn't know what she is doing, she will not be fully compensated.
She can't appeal the USCIS's decision, if that is what you are asking because you will need to show documents that she was not out of the country for more than 6 months. In this instance, she was clearly out of the country for more than 6 months. When did your mother return? Depending on when she returned, she has to wait and can file according to what my colleagues have advised.