Being that both of my parents dated after they were divorced, and both played the "family man/woman" card by letting their cute kids play together, I can say it doesn't work. It's not a good premise to base your relationships on and your kids, as long as they're old enough to understand that a new woman is in the room, will realize what you're doing and resent you. Just be a man and be direct. You don't have to ask for a date, just say you'd like to get to know the sister better.
That's a good point. They're not used to a woman being around daily anyway. Their mom is only around every other weekend. But I see what you are saying. There's a gathering on Saturday that I was gonna see if she was going to. We're both kidless this weekend, so that is a good opportunity I guess.