Here's another idea, if you don't feel you can leave your 9 y/o with the 17 y/o: What about making arrangements with the parents of a classmate to sleep over at the other's house that night? You could offer to reciprocate for a weekend when they need a getaway or something.
I think I'd be hesitant to talk about changing the conditions of my job with the way the economy is right now.
I do agree with tjp, too, though--unless your 17 y/o is irresponsible, it seems like something s/he should be able to handle for one night. And yes, a reward of some kind would be appropriate.