Most Helpful Girl
Yeah, I think that's a bit weird. It's better to do that when you're alone with that person. If you feel that you never see her when she's alone, ask her if you can talk to her and maybe walk away from either of your parents.
Most Helpful Guy
If you man up and charm your way through the awkwardness, you'll simultaneously win her over, and win the parents on your side in one move. It's a golden opportunity, in my books.
For example, just say to her parents in front of her, "Hey, I'm just going to say it. I find your daughter very attractive, and I'd like to take her out sometime. Maybe start with a coffee, maybe see a coffee, and then do something fun and chill out for a bit so I can get to know her. I don't plan on doing anything weird, and I promise to get her back at a reasonable hour. What do you say?"
And if they ask or hint why you aren't asking her instead, just say "I've wanted to ask her directly, but it doesn't seem like I can get any 1 on 1 time, so... here goes."