I would definitely quit. I guess you will really need the job; and you have your own valid reasons to keep staying from your point of view. If I were you I definitely leave no matter what. Sorry to tell you but a position like that it's not worth at all. Physically and emotionally. But I respect your decision to stay. It's your own decision. I wish you good luck anyways.

My fellow nanny - I have as much experience as you do in this field and what I come to understand is that with some families it won't be a paying role but rather a role that requires the heart to go above and beyond regardless of the monetary compensation which you have done extremely well till this point. The real question is really about if you are willing to stay for the children despite those circumstances or not?