You sue the person that hit your wife. You will serve the complaint on that person and, just in case, also send a copy to the insurance company to make sure they cover the claim.
The above answer should not be considered and does not constitute legal advice. You should not rely on any of this advice because each case is fact specific and could be subject to different local, state, and federal laws. No attorney-client relationship exists based on this response.
You sue the person who hit your wife, not the insurance company. The insurance company has a duty to defend and indemnify its insured. If the insurance company does not fully pay for the damages you can prove, then you can also collect against that person individually.
You sue the other drive who will have to personally appear in court and defend their actions. No lawyers allowed in this phase of a small claims case. The maximum that you can win in small claims court in California is now $7,500.
Before taking this step, however, it would be prudent to speak with a personal injury lawyer in your area to determine whether the value of your wife's case may go significantly beyond the $7,500 threshold. Most personal injury attorneys will offer a free consultation.
Please see links below for more information regarding Small Claims Court in California.
Sign up to receive a 3-part series of useful information and advice about personal injury law.