Spanish to English Art/Literary Poetry & Literature short story

The phrase I'm having trouble with is "salir detrás de". It appears in a short story written by a Spanish author. It is about a man whose wife leaves him and takes his children to live with another man. The breakup is brutal and abrupt, the man is shocked. I've included the sentence that precedes and follows the sentence containing the phrase in question:

"Pensaba también en su familia, pero no veía que podía hacer para mejorar su situación conyugal. *Salir detrás de* su mujer hubiera sido una gran humillación y no hubiera servido como nada. Belinda era la obstinación en persona."

Some ideas:
- does he mean that to go out in search of / to follow his wife would have been humiliating?
- or to got out with someone else behind his wife's back would have been humiliating?

thanks for any ideas