What do you think of this beginning?

Well, the father switched from calling her a "punk" to a "silly little girl", maybe try not to change to often? The characters CAN be believable, if you just change it up a bit. Have the man giving away the car have an explanation on why he's giving it away so easily. Just giving it away because it never works is not so believable. Have him go "Give me twenty buck and it's yours." where the girl still has to pay something.