insurance co. Liberty Mutual tried to pull the same thing with me. We got a new car and did NOT want my teenage driver on the policy. She would not be driving it. LM said she had to be on it since she is a driver in the household. When push came to shove, they gave us a separate policy for the new car with just my wife and I on it. You could go to another insurer and get a separate policy for your daughter's car too.