If you haven't ever spoken with your nanny about what happens if a day that you happen to get off of work (for holiday, office closure, etc), then that conversation is overdue in order to make sure you are both clear on expectations.
I personally see "holidays" that we professionals get off of work, paid by the way, should be paid holidays for our childcare workers. They don't get paid much as it is (relatively speaking) for a tough job and to expect that just because we are home one day they shouldn't get paid isn't fair.
So, with my frame of reference, the two days that happen to fall on Mondays should be paid or not paid based on whatever you set as expectations on days "you don't need her to come".
Given that, the Monday argument your husband has would not be relevant. Then it's a question of what you want to do for an end of year thank you.
I agree that one week per year is standard, so two days in this case. But if you haven't had her all year, that could be reduced also. Whatever you decide to do, it should be with gratitude for the work she does for you in teaching and caring for your daughter.
Good luck with your discussions, whatever you decide.