We own a car that you allow your mother to drive as her primary vehicle Is it okay to insure the vehicle under your name but put her as a rated driver on the policy if she doesn't live with us?

No. You cannot insure something that you don't own. This is a fact of life. The insured and the vehicle owner must be the same with the only exceptions being members of a household immediate family, which does not include parents, brothers, sisters, friends, or boyfriends of the insured. If you are insured and you add a car owned by anyone except your spouse or dependent children living in your home, and the car is damaged, the insurance company cannot pay you for damage to a vehicle you don't own, and cannot pay the owner, because they don't have an insurance contract with the company. There is no way around this. If you add a vehicle you don't own to your policy the company will not pay for damages to said vehicle. They cannot legally do so. It makes no difference if the owner is a rated driver or not. You mother must have her own policy.