Attempted measured response to follow:
It is extremely unfortunate that you were involved in this accident. I really hope your wife’s back is not permanently impaired, although it would not be unusual for her to have some long term, recurring, or even permanent symptoms that adverely affect her life. Also, as she ages she may develop symptoms she would not have had or at an earlier date than absent this traummatic event. And I certainly hope your child has not been significantly or permanently affected.
So how do you figure how much this accident cost you - how much would it take to make you whole? Unfortunately, my experience is that while legal proceedings do the best they can, most people do not feel "whole" after the process. They generally would have preferred that whatever brought them into court did not happen, over eventually receiving an award. You have car and health insurance, so at least that's covered. Both of them will subrogate against the other driver to whatever extent possible. Hopefully you car insurance covers replacement cost. If not, that certainly is a amount you could look to recover. Add in your deductibles and copays (which you could get back as a result of your insurance company’s subrogation action).
So what are your additional, non-monetary costs? And how much would it take to fairly compensate you for them? Unfortunately, my experience is that unless you are really messed up (and thank goodness it sounds as though you weren’t) the payback is not going to be worth the time and effort it takes to pursue the action. As you said, a few thou isn't going to drastically change your life. Meanwhile, you WILL have to document EVERYTHING for which you hope to recover. Use a very rough guide - estimate your expenses (car + meds) and multiply by 3. So 1/3 goes back to your insurance company, 1/3 goes to your atty, and the remaining third is yours, pain and suffering, etc.
We went through a similar experience a few years back. Wife was diving the station wagon, stopped at a red light, got rearended by a truck being driven during the course of business (can you say “deep pockets?”) Shattered the rear tailgate and crumpled the back end, but fortunately no injuries to the 3 young kids. My wife, who has a prior history of back pain, suspects she might experience some more problems as the result of this accident, but how can you be sure? And she still gets around pretty well. Gives her a reason to ask for more back rubs! 
Bottom line, we could have sued, and made a few thousand - automatic. Our recovery would have been lower than yours, cause the car was repairable. My wife went to the doctor, and everyone checked out okay. Car got repaired, and we got out deductible back after the car insurance successfully subrogated. If we wanted, we could have gotten each of the kids cute little cervical collars (oink ones for the girls…), gotten a family plan at the chiro’s, etc. But we didn’t want to spend the time and effort building up the claim. If anyone out there wants to say that it is unheard of for people to do such a thing, well, my experience is different than yours.
In my opinion a lot has to do with your pain threshhold. Or your desire for vengeance. Or how protected and pain free you expect your life to be. Shit happens. And you move on. If I slip and fall, even if I break my leg or something, and it is someone’s fault, well, my insurance covers it and that type of injury heals.
That was the intent of my initial post - you should sue if you have been injured in a manner that legal action is needed to more closely make you whole. Unfortunately, there is a percentage of our society who believes that litigation automatically follows an accident.
Litigation is not exactly a laugh riot. Weigh whether the effort involved is worth what you can realistically expect to get from a fully successful lawsuit, both financially and otherwise.