Are two-income families the result of economic desperation?

No:

The big increase of women in the workforce can be traced back to an increasing number of wives of well-to-do men pushing into the labor market.  These women typically earn high hourly wages.

Meanwhile, among women whose husbands earned hourly wages in the bottom fifth of the distribution, the growth in labor market participation slowed down — contrary to the overall trend.

In 1969 the annual incomes of working wives showed no correlation with the wages of their husbands.  Wives of high-income earners earned above average wages, but they worked fewer hours than average.  In the late 1980s, however, wives of high-income earners worked almost the same amount as wives of husbands with lower incomes.

That is from the new and excellent Cowboy Capitalism: European Myths, American Reality.  Here is my previous post on the book.