I think this is a rather complicated question to answer totally, but if a file is downloaded and then deleted, there are ways to find it, but I think if you started doing this it would be bad for mother/daughter relations
Limewires history of a session is deleted when you close limewire.
If you don't want your daughter to use Limewire, set up separate user accounts with you as the administrator. In Mac this will stop anyone else installing a programme without your permission, not sure with Windows.
In short, the only way to know what she is downloading is to watch her.
If the file, complete or incomplaete is still on your computer undeleted, you can search your computer for any files added in a given time.