Twice a week, at around 11 p.m., Jeff Goldstein stretches out, turns on his spa playlist, lights a candle and gets a 90-minute massage — courtesy of his children’s nanny. “At first, [I felt] a little awkward,” admitted Goldstein, 41, who has two kids and co-owns the celeb-favorite clothing boutique Blue & Cream in the Hamptons and East Village with his wife, Samantha Greenes. “But then, it was so, so good.” Having a nanny who can teach your kid a second language doesn’t cut it anymore in New York City’s elite circles. Now there’s a fleet of super nannies who...