Just remember, you are 100% responsible for anything that your internet is used for... I am VERY uncomfortable with anyone getting on my computer and who know what else she will do on it if you allow her to use it. She has already proved she isn't trustworthy and a user. Give her a inch and she is going to take a mile.

She already has shown she had no considerations for your feelings so why should you care about hers. I'd tell her "No" and offer no explanation as to why.