K.W.
The State Department sets the rules for au pairs. Hosting an au pair is like hosting an exchange student, except their primary responsibility is child care.
An au pair comes to the States as part of a cultural exchange program. They are generally in the States for a year, after which they can extend for 6, 9, or 12 months. The costs pencil out to approximately $1480-1500 a month, plus you provide a private bedroom, food, and a phone for their use. If they drive (not all do), you'd probably want to put them on your car insurance. Plus you pay up to $500 for them to take a class (required by the State Dept) during their stay. They are restricted to 45 hours a week of childcare plus limited light housekeeping duties/shared family chores. They are not a live-in-maid. If you go through an agency (I'm not sure there is another legal way to do this), the agency provides an area rep who looks after both the family's and the au pair's interests.
From your description, it sounds like your needs wouldn't fit an au pair, but might fit a temporary nanny. They are different.