You absolutely sure you love her?

To me it sounds like you just don't want her to be with another one, and now that she's shown interest somewhere else, THEN you love her.

Frankly I don't understand why she was with you for so long, I mean it's like dating a 2-sided person.

Here's what you do:
If you sure you love her, then you take her word for it, you know trust her on making the right desicion.
And if you don't love her, then you move on with your own life.