After dropping off their children at their East Side private school one morning, Betsy and another mother shared a secret. “It was one of those things where you circle around each other,” Betsy remembers. “I assumed they had a pretty conventional marriage.” By that she means, as with most of the other families at the school, the other woman’s husband was a chest-beating breadwinner who set off for Wall Street each morning in his Town Car to bring home the six- or seven-figure bacon. Or, alternatively, both husband and wife slaved away at medium-to-high-powered jobs, neglecting their children, to pay...