It's not money for sex, you're paying them to leave. Besides, do you really want to take advantage of someone who's obviously desperate? Up to you. But for me, I've (and she) always left kids out of it. Just not fair to them.

My advice: tell her straight out. I learned a long time ago to never promise or imply a future I couldn't/wouldn't deliver. But personally, I'd extract myself as soon as possible, if for no other reason than the kids.