Are you joking? Lieing about where she is going, and about who she is going with, that is a problem. In a real relationship, lies aren't needed. She is trying to hide something. Not saying she has cheated yet, but she obvoiusly feels she is in the wrong, or else why would she be lieing?
I do agree though, the spying is a little overdone. I look at my GF's website history sometimes, and email if she leaves it open i'll take a quick look at whos' emailing her... but you have taken it to the extreme. I completely understand why, and how you feel, but as Asip4u and I have said, you need to be very careful with what you are doing, because if she does find out about the spying, it will be detrimental.