Mr. Hoffman is right, these cases are incredibly complex and it will take at least one (and possibly several) attorney appointments before you know if this is worth pursuing. Your attorney will need your mother's complete medical records and history, but that doesn't mean you should wait to see someone until you have those in hand. Make an appointment tomorrow and see a few attorneys asap.
Right now, the best thing you can do is inform your personal insurance as well as the insurance on the rental car, preferably in writing. If the damage is minor, you might want to work out an agreement to pay for some or all of the damage. You would want a written agreement saying you agree to pay x amount and he agrees not bring any suit or other action against you in the future. Either way, a quick phone call or consultation with a lawyer will likely be helpful.
What you need to do right now is make sure your mother gets the best treatment possible and consult with a local attorney. Your best best is the local bar association or a friend who had a good experience with a local personal injury lawyer. Just so you understand, how "greedy" or nasty the CEO is has nothing to do with your mother's case.
Depending on what court you are in, different levels of disclosure are required. Generally, you should be given notice of every witness the other side intends to call and a chance to question the witness. I recommend contacting a lawyer. The person who represents himself has a fool as a client.