That is a tough one....and there really is no simple way to go about it. I feel the best route to go is be honest with the kids. Tell them that mom is busy and you have no idea when she will be home.
I like that you expressed your feeling as your wife has requested of you.
I am going to ask something, but you need to bear in mind that is has no affect on what YOU are doing. Do you think she may be having an affair? Understand that doesn't change the DB things for you! Other than if it is a complete deal breaker, but of course in your situation that would be the pot calling the kettle black. That said, I am curious.
