I hope I can explain this. Teachers pay and conditions are a bit complicated. In regard to unpaid hours, there is no such thing in teaching! Teachers are required to spend 1265 directed hours per year (classroom teaching, parents evenings, training courses, staff meetings) plus whatever is needed for planning and preparation. You could go into school every day of the year and it would still only be part of the contract. There are no days in lieu.
Supply teachers are paid by the annual salary divided by the number of school days, so in order to cover the cost of DILs absence the school would need to deduct this amount from her salary. It used to be a 365th but obviously then each day of absence cost the school money which in a bad year could mean the loss of a classroom assistant when it came to balancing the budget.
Personal responsibilty days only existed in a few LEAs which recognised that women mostly bear responsibility for family crises and tried to address this as a matter of inequality. Now schools have responsibilty for staffing budgets I don't think there's a school in the country that could bear that cost.
Of course if your DIL is in an Academy they can set their own terms of employment, as they like
Hope this clears things up a little.