Who's at fault if you rear end someone who does not have a driver's license or insurance and does not have permission to have his mother's car?

You are At Fault for "undue care and attention" but the driver of the car you rear ended will also be charged without having a license. The mother of the driver will be fully responsible (insurance wise) and if you are lucky will have to pay for the damages of your car. It depends on how the courts see it. If the damage is minimal and the mother of the car is willing you can settle out of court (a better way to go) and she can agree to pay any expenses to the damage on your car. Don't do this if there were any injuries caused to either you or the driver you hit. Go to court.