An au pair isn't going to save much money if you need to spend $200K for a bigger house with an additional bedroom.
Is au pair the standard term for live-in nanny? It sounds like a day-time nanny plus possibly some other help so they are not swamped would be fine. Having a pile of hired help is still a lot less expensive than buying a new house, not to mention a lot less disruptive. Plus the new house is forever (or until they sell again) while hired help can be cut back as the need decreases.
No, an au pair is not just a live in nanny, it is a program that brings young (most countries have an age range of 18 to late 20s -ish) qualified child care candidates to host families via government designated agencies- there are rules, and in the US the au pair program is administered by the US Department of State. Rules relate to remuneration, duties, education, hours worked. Au pairs will do light duty chores that relate to the kids- preparing meals for kids, doing kids laundry, etc. They are not required to do stuff like clean bathrooms or tidy up a parent's space or serve as general housekeepers. In the US, the au pair is also required to fill an small (6 credit) academic requirement during their stay.
My sister uses an au pair for her twins in the bay area. She already had sufficient space in her home and the day care costs there are outrageous, so it made a lot of sense. Plus, IDK if they just lucked out, but their au pair is amazing. So good with the kids, a wonderful person, she's really like part of the family. I think her au pair time has run out but she is still able to stay on a student visa, or while awaiting results of the student visa application or something like that. She's been with the boys since the were 9 months and they are now 3.5.
Also, their au pair knows other au pairs that have really sweet gigs. One is an au pair for a single dad w/ joint custody in hawaii. The kid is only with the dad like, every other week or something, so the rest of the time she just lazes around on beaches. She knows another au pair who's "child" is like 16- she's basically a hired playmate/chaperone for the teen. No screaming kids or changing diapers. Although I guess teenage girls sometimes aren't all rainbows, either...
I wish I had known about the au pair program when I was younger. I know a recent college grad that was an au pair for the summer in spain. Seems like a good way to see another country for an extended period!