If only one parent is insured by a particular insurer, that insurer will charge the additional premium to the insured unless the parents agree to have their own insurer apply it to their policy. However, not all policies are the same. Check your policy language or contact your insurance company for details. If you don't list your teen on your policy, be prepared for the potential consequences. Cancellation, nonrenewal, and surcharges are among the unpleasantries you may face if your teen is driving your car regularly without your paying the extra premium.
Some insurers require that all drivers be named on both policies.
Some insurance companies will cancel your policy for misreprentation if you do not disclose your teen driver during the application process or when he or she gets a driver's license. Even worse, if you file a claim for an accident your teen has, your premiums could go up as a result. And then your insurer could nonrenew you. Some insurers require that all drivers be named on both policies, no matter how much time they spend in a household. Whether a child is at the house on the weekends or full-time, if the visiting teen customarily operates the covered vehicles, the insurer has the risk exposure and thus they charge for that exposure.