Personally, I couldn't afford to take the pay cut. And I don't like the feeling of being on-call - set school vacation days/holidays/teacher conference days are one thing as they are all scheduled in advance, but having to be available for sick days when you may not find out until the morning of the same day you need to be at work? No. It wouldn't work for me.

Why not interview with other families and see what's out there.
I got a job before where I had a school schedule colliding with their schedule for the first 6 weeks and be use they really wanted me, they worked around my school the first few weeks.
I'm sure if you find the right family, they would honor your precisely planned vacation.