You're talking about two different things: guaranteed hours and paid holidays.
Guaranteed hours would mean you are paid for each T/W/TH that you could normally expect to work (day before Thanksgiving, yes; Christmas/New Year's, no).
Paid holidays means that you are paid even when a major holiday falls on one of your work days.
You are a very part time nanny. I suspect you will have success with the guaranteed hours request, but will meet with resistance on the paid holiday request. Paid holidays are not usually a perk of part time employment. If they really want to keep you happy, maybe they'll agree.
This is a great post. Very true.