Does the nanny work for them in Chile, also?  What you have is a nonresident alien paying a domestic servant (nonbusiness employment) who is also a nonresident alien.  If you look long enough you might find something that applies to this situation -- I doubt that this country has an interest in taxing it, or paying benefits to the nanny if she keeps coming back part-time in future years -- but then if you found it was taxable,  you would also have to check the tax treaty with Chile to make sure there is no exception.