@ Judy: Hehehe.... asshats. Funny.

Yeah, I have to admit that it doesn't usually get better when things start out like this!! I would likely care for the children for two weeks, give 2 weeks notice at that point, and advertise immediately.
If they are looking at childcare ads, then there is probably a reason for them too. And in any case, there are a lot of ways to advertise. I am sure you could arrange it so that it isn't likely that they would see.