I am not sure I understand? Your contract says you charge for stats, but because of her previous dc experience (but not with you), you said they DON'T have to pay them? I am confused.
If you told her she doesn't pay for Stats, then I guess she doesn't.
But if it is in your contract, and you have not made some sort of special exception for this family, then enforce your agreed upon contract.
Most people get paid for Stats some how, some way. My husband doesn't, but that is because he is a business owner and that is part of life for us. I don't complain about it.