Without being too dramatic, I would contend to you that this is one of those handful of DEFINING MOMENTS in your life. How you respond to this will say everything about your character, your morals, and how high of an integrity bar that you set for yourself.
Think this one over carefully, and then respond with absolute CLARITY to your wife. Every hour that goes by since she lobbed this amoral grenade into your lap, starts to define YOU and what you stand for.
"What is best for my kids is best for me"
Persevere = happily being patient over a long period of time