Maybe call it House Manager... the job title is not important but perhaps looking at it from that perspective will help both of you.
They are there to manage the house and everything that it involves, including the children. It may involve supervision of other staff... though probably not if they are the only one there but if you have a cleaner come in for a few hours a week, they may talk to them, though wouldn't really supervise them as the cleaner is not an employee.
Keeping things in a reasonable state - so light cleaning, sweeping the floor, vacuum carpets, general tidy up.
Making the beds, changing the beds, laundry of bedding.
Children's clothes laundry, making sure they have everything they need (beaver, rainbows, brownies, cubs, other youth group uniform).
Doing additional food shop (beyond that which you get delivered).
Making cakes (or buying) for the school cake sale.
Going to school events such as sports day.
Being in for plumber, electrician, whomever is needed to fix something.
Being in for signing for a delivery (if it is known something is coming - don't expect them to be at home all the time).
Cooking for the children, possibly things for you as well.