1. Grandma locks her out--and allows her to come just to porch to recover any of her stuff--but not inside. Grandma keeps her out and calls cops if she forces her way in
2. If she stole GM's car then GM reports it stolen and follows up with police action etc.
3. GM avoids like the plague any actions which could be seen as creating a tenancy status for this relative--GM accepts no rent and enters into no agreements to allow her to stay even 1 hour and gives her NO keys etc. Problem is that a guest of 2 years in many eyes looks and smells like a tenant--and its improper/illegal to merely lock out a tenant---GM may need to take a calculated risk as to guest status and play hardball. If she gives GD notices like a tenant then that may hurt GMs stance that she is a guest.
Absence of rent is not absolute that there is no tenancy status..there could be more subtile forms of "consideration"--but generally to have a lease ,a form of contract, requires consideration--no consideration often= no contract=no lease.
But NJ gives tenant slots of rights so it might even be wiser to have GM spend a few bucks with skilled legal counsel on such L-T issues...