If you had liability insurance at the time of the accident, you should immediately inform your insurance carrier of the judgment and ask them to pay or to have the default vacated; the insurance company can pay for the attorney.
Your mom had a parking lot accident, and likely did not tell the other owner what happened because she did not see any damage. The questions are how much is her deductible; and whether its worthwhile to make a claim when she will end up paying more for the repairs in insurance than she would if she just paid for the repairs herself. The insurance company can deny the claim if the claim is false.
You have two options, pursue the owner/driver or put a claim on your insurance. If you put a claim on your insurance, your insurance company can then fight it out with the other company and perhaps get you back your deductible. If you are unsatisfied, contact an attorney.
If you have collision coverage on your vehicle, you can file a claim with your insurance company; your insurance company will pay for the damage, less any deductible. They can go after the other driver and her insurance company. You can also go ahead and file suit against the other driver, and get a response that way. If you do not get anywhere, contact a lawyer with experience in handling insurance car wreck claims.
Of course the employer can deduct premiums from your paycheck to pay for health insurance. The better course would have been to begin deducting premiums from Jan 1; but I am not aware of any provision which would preclude the employer from catching up on premiums due.
talk to an attorney in your area that works on car wreck cases. You will probably also need to let your own insurance company know of the accident. If you have comprehensive coverage, your insurance company will fix your car (you will be out the deductible) and go after the other guy.
The health insurer is usually entitled to reimbursement. The auto insurer is not entitled to reimbursement. the statute is 36 O.S. 6092, and has not been amended since 1971. the double dipping, then, is between auto insurance companies, and not between your health insurance and any other insurance company.