There is no law that tells police how to investigate a case, but I would expect they would investigate whether the driver was impaired. There are a number of laws that govern when and how such testing can be performed. A criminal lawyer with DUI experience would probably be the best person to answer your question.
I assume this is about damage to your car and not personal injury to you. If your own insurance company won't or can't get Progressive to admit liability and cover your vehicle repair costs, you have the right to sue the woman in small claims court. Talk to your insurer about doing that.
If you suffered an injury, see a lawyer and he or she can both purse the injury claim and guide you on how to proceed with the vehicle damage claim.
You won't accomplish anything if you want your complaint to be anonymous; you would have to withhold not only your name but also the date, time and location of the detention (otherwise they would figure out who you are from their records). If you withhold all that, you give them a good excuse to simply ignore your complaint.
Your fears about retaliation may be legitimate, but if you really want to prevent future occurrences like yours, you would have to provide all the information necessary to investigate the incident. Departments often have forms, paper and/or online, you can fill out to start the process.
I do not agree with the answer from the Florida attorney - reporting an accident with no damage is pointless and the officers will probably not even take the report down, but there is more you can do.
You can of course report this to the school's principal.
You also have the right to seek a protective order from the court that requires the person to stay away from you and your family, although the judge will have to be creative since you have kids at the same school. If you want to get a protective order, call, visit or look at the web site for the Riverside County Superior Court and you should be able to get the forms to fill out. You will need to file the forms and provide copies to the person against whom you seek the order. There will be a hearing and the judge will ask both of you questions and rule accordingly. If you get a protective order and the person violates it, you can call the police to have it enforced.
These are questions for the lawyer that is representing your daughter. They should be conveyed privately and not posted over the internet for all, including opposing counsel, to see.
This is not necessarily a silly question, but it is silly for you to expect a lawyer to spend time answering it when you won't spend the time to provide details.
There are exceptions to the rule, but normally claims arising out of the same circumstances can and should be filed in the same case. You can't sue a state or its agencies in federal court, but you can sue individual state employees in their personal capacity in federal court.
The plain language of the statute, Civil Code 3333.4(a)(2), appears to extend the denial of general damages to the owner who is riding in a car as a passenger, but this is a complex question that would probably require a bit of research - I suggest you seek counsel who can research the question in the course of pursuing a claim. You seem to be on top of things and realize that even with Prop 213 you can still recover economic damages, including the cost of medical care.
I want to add, however, that it makes sense to deprive the owner/passenger of general damages in the situation you describe. Since the owner is sitting in the car, he or she obviously must have expressly allowed the excluded driver to operate the car, knowing that would render the car uninsured for liabilities to injured third parties. There is no "technical" insurance here - if the driver injured or killed someone, there would be no insurance for that. The statutory purpose is advanced by penalizing the owner/passenger for allowing that to happen. That's probably the way a judge would see it.
There are all sorts of attorneys out there. Some will take small cases - others will not. Obviously you spoke to someone who chooses not to take smaller cases; you need to find someone who does. As others have said, you do no one a favor by getting unnecessary treatment just to make your injuries look more significant, especially since you have just posted your intention to do so on a public web site.
No it is not worth the time and hassle to sue AAA simply because they provided bad service. It might be worth it to sue them for the injuries you suffered as a result of that bad service, but if you don't think those injuries are serious, I would move on with your life. You have two years from the date of the accident to figure out whether your injuries are worth suing for.