My parents were super overprotective, and while not particularly strict per se, I never really confronted them about their rules while I lived under their roof. I know what it's like. It's not only fear of punishment, when you have parents like that you're terrified of disappointing them. I didn't really get out from under that until I moved out, and to this day they still don't know about all my tattoos/piercings, among other things. I'm so conditioned to doing what they say and hiding it when I don't that I still actively hide these things, even at 23. That said, you can be sure I hid several relationships from them when I was younger, and I can tell you from personal experience that that shit just doesn't work out. Hiding it doesn't necessarily mean she's playing, but it does mean than she, and probably even you, are too immature for a serious relationship. I'm not saying don't enjoy it while it lasts, and I'm not saying that you shouldn't try to make it work... by all means, do. All I'm saying is that unless the situation changes, it's not going anywhere longterm. If you're not ready to admit to your parents that you're in a relationship, you're not ready for a relationship. It needs to be something you can be proud of and open about.