In most states there are ways in which to get the licensing authorities involved if you believe an elderly parent should no longer be carrying a driver's license or be on the roadway due to their failing abilities which make them a hazard to themselves and others.
How you can stop your 82 year old mother from driving depends upon the laws of your state since the steps to take vary from state to state but typically you can get information on this topic from your Department of Motor Vehicles or Highway Safety Agency. Here are a couple of state specific examples.
In Ohio, the administrative code allows for relatives, friends, neighbors to take action (turn in a risky driver) by submitting a signed request for an investigation to the Bureau of Motor Vehicles (BMV). The letter needs to provide them with enough information of personal observation of unsafe driving so they can require the person get a medical statement or take a driver license re-examination test.
Specifically the BMV states on this issue that the Ohio Motor Vehicle laws allow the Registrar of Motor Vehicles to require an Ohio licensed driver to submit a medical statement and/or take a driver license examination upon receiving information giving "good cause to believe" that the driver is incompetent or otherwise incapable of safely operating a motor vehicle. The Ohio Administrative Code states that "good cause" is considered to be a request for recertification received from a law enforcement agency, court, physician, hospital, or rehabilitation facility. To take action on a request received from a law enforcement agency or court we require that the agency or court has had personal observation of the subject's driving or personal contact with the driver. We cannot take action on the recertification request if it is based solely on the person's age or hearsay.
The Bureau will also take action on a written and signed request submitted by a relative, friend, neighbor, etc. However, the BMV is required to first conduct an investigation to determine if there is sufficient cause to require a medical statement and/or driver license examination. Age cannot be the only basis for the request.
In Ohio the BMV is legally obligated to inform the driver who is the subject of their investigation or recertification procedures of our source of information. Therefore, before an investigation or any other action is taken on request received from a family member, neighbor, friend, nurse or social service agency, they must receive permission to use the letter writer's name as our source of information. Information received from a physician is considered confidential. So unfortunately if you live in Ohio, or a state that has similar laws, whoever writes the letter will be identified to your mother. Some states may allow the person to remain anonymous so when contacting your DMV to find out how to about your mother's driving abilities ask if she will find out that it was her children that turned her in.
The Ohio laws that govern driver license re-examination and medical recertification of a driver do not involve vehicle registration privileges or license plates. Therefore, registration privileges will not be affected even if driving privileges are denied. You will also want to check on this issue in your state, or in your mother's state if she lives in a different state than you and your siblings. If she is able to keep the registration on her car valid and you can trust her to not drive it if her license is taken away than she may want to keep it so that you and others could driver her around.
Losing their ability to drive can be painful for seniors but if they have other forms of transportation available to them it can help ease the pain. If your mother will not drive the car than leaving it at her house to be driven may be one choice. If she keeps it registered and titled in her name though you and your siblings will need to help her find insurance that will exclude her as a driver (if she no longer has a valid driver's license) and will instead allow her children or whoever will primary drive her in the vehicle to be added to the policy as the drivers. The policy would then be rated by the driving records of those listed on the policy as the drivers.
Just as another example, Florida allows for those that know of an unsafe driver to make a report to the Department of Highway Safety and Motor Vehicles (HSMV). The report needs to be in writing and give specific details of the person. These reports in FL are kept confidential and shall only be used to determine the qualifications of the individual to operate a vehicle.
Senior drivers that are a danger on the roadway do need to be reported to the licensing authority so that the situation can be investigated and the person's license revoked if necessary. Your state's DMV should be able to advise you and your siblings on how to report your mother and what steps you and the state can take so that she does not continue to drive.