Having been through a simular type accident. Do the following.
First get a copy of the police report and make sure it states that your wife was not at fault.
Second, you will start to receive lawyer letters trying to solicit your business. Kep them and the report in a folder with the report at the bottom. Also add doctor bills after the report.
An insurance adjuster for the person that hit your wife will contact you to setup a meeting. Your insurance will assign an adjuster as a rep to guard your insurance concerns first and your concerns second, but they will help. Your insurance card should have a 24 hour number to call. Call that number.
Whether or not you get a lawyer is up to you for that first meeting but I met the first time alone.
The insurance adjuster for the other driver tried to make it appear it was my fault.
Now this is where the lawyer letters and report in the folder comes in to play. I made the show of flipping through the letters, about twenty, before getting to the police report on the bottom.
The adjust read the report that said in big bold letters 'Not this driver's fault.' Signed by the officer. Case closed.
Adjuster then asked what the other papers were. I said ' All the lawyers that want my business. Do you want me to call one?'.
Long story short, adjuster and me came up with a contract. Car fixed to my satisfaction not spec, made them fix some issue with my car. Two years of orthopedic doctor services and twenty grand expense money with punitive expense of thirty grand for just pissing me off.
When you go in to resolve this go like you are going to war. Take not prisoners and do not put up with any bull shit. Get an opinion free from a lawyer.