@bathsheba,
This doesn't seem like a computer problem at all.
It seems to me that your daughter is acting irrationally which means that no matter what "evidence" or reason you offer, she is going to accuse you.
My advise is that you simply refuse to play her game. Assure you that you aren't spying on her... and that you have no interest in doing so. If she doesn't accept this, then it is her problem.
It seems to me you have far more important things in your life.