Couple of thoughts.
One, you are right to tell your children the truth. What hurts your children is the reality of consequences not knowing WHY they are having to accept the loss.
The only thing offended here is your wifes PRIDE and EGO.
She does not want to accept responsibility for choosing to hurt her children in order to please her lust.
Two, you have often been a very "grey" thinker in the past and it looks like you have been surrounded by other grey thinkers.
The grey thinkers are never going to support you taking any action that results in "discomfort" for themselves.
No amount of explanation will pursuade them.
They much prefer to tell the children [the people who have NO choice] to suck up their loss and smile...that they are wrong to feel anger, loss, and to ask questions like...why do we have to do this? The answer to that question is that they don't HAVE to do this...she WANTS to do this and she doesn't care what they want or what is good for them.
Grey thinkers are NEVER going to support the belief that a person is bound to do what they no longer FEEL like doing.
If you want to find support for black and white concepts you are going to have to find a new social niche.
You have been badly used with your cooperation. This is weakness and uncertainty and not much else.
They LIKE you to be weak. They LIKE you to be used.
When you are no longer available to be weak or used they will no longer like you.
I'm sorry but that's the way it goes. You aren't playing the game by their rules anymore and they'd rather kick the table over and stomp off than respect your change of heart.
Your children knowing the truth about their lives will bring some uncomfortable questions into play and may even ask them to do what they do not feel like doing.
Grey thinkers believe that if you can conceal the sickness you can negotiate the consequences.
Not true...man does not have power over consequences...only over choices.
Stand in defiance of God at your own peril, yes?