I agree with Jimmy C. I assume you didn't hire the girl through her mother, so I think it's totally inappropriate to fire her through her mother. If mother and/or daughter scuttle the friendship over a justified firing, was there a real friendship, or just someone whose company you enjoyed?

There's always a last chance. Maybe she's used it up already, and the next step is dismissal. Maybe she's got one more whack at it due her, with a zero tolerance policy. Step one: decide when/where her last chance is/was. Step two: communicate to her--it should be firm, nice, and somewhat blunt, and leave no doubt in anyone's mind. Step three: follow through.

Above advice valued at the standard two cents--on special today, free! And worth every penny!