A couple of things to consider. First, you don't need to pay taxes for au pairs like you do with regular caregivers. Since this is a relative living with you, you may or may not be obligated to pay taxes. Given the relationship, doing this under the table may work for you.
Au pairs are restricted to working no more than 45 hours per week. They are paid approx $200 a week (the extra $150 a week goes to the au pair agency for recruitment and paperwork costs). They get free room and board. They are not housekeepers, and are asked only to do chores related to the kiddos (e.g., kids laundry, picking up after kids, cooking for kids). Again, since she is family, she may also be helping you as a family cook and clean up after dinner. But I would recommend against having her do more.
It sounds like a great idea. I hope it works for you.