[Eternal]

The only thing you can do is let your parents know that you want to be there for your girlfriend and support her because she's probably very nervous about the surgery. Ask them to put themselves in her shoes, wouldn't they want their partner there with them?
If they still say no, there's always a next best thing. Call her when she wakes up, or make her a present for the next time you see her. You could make her a get well cake, a mix CD for her to listen to while she recovers, or write her a poem. There are lots of possibilities, and it will show her you care even though you are unable to be at the hospital with her.