I don't see any reason why he can't pay her to do anything he wants (watch kids, clean house, etc) as long as he pays household employer taxes and issues her a W-2, and she reports the income on her own return.
However, as noted, he can't then claim her as a dependent, and any wages he pays for child care to a related caregiver are NOT eligible for the dependent care credit or the use of an FSA.
So it's legal, but it's dumb, and will cost money for no benefit.
