Make sure they don't try to bundle the property damage (your car) with the medical part (your wife) into a single process, they should be handled separately.
Whatever you do, don't sign off on the medical for at least a couple of weeks. Sometimes it takes that long (or a little more) before the real pain in her neck or shoulders may show up.
Being rear ended hard enough to total a rust free Buick Park ave was a pretty hard impact, it is not out of the realm of reality that a serious back or neck injury may show up. Once they get you to sign off on the medical part, there are no repercussions available for you. Gene