From standpoint of IP law in US, does work done at home in the off hours belong to employee or employer?

There are lots of teacher tip guides and books out there so I highly doubt any schools really have the time or funding to hire lawyers to argue they deserve a piece of her pie. If she thinks this is a book that's going to make her a millionaire, then maybe you want to hire an attorney to talk it over or talk to the school first about it and see what they say.