Anyone remember debate class?
Given, you should have been up front years ago
Given, what your wife did was childish and unnecessary
Given, you should not have lied
Given, revenge won't help the situation (see childish and unnecessary above)
Given, you love your children (your wife right now not so much but we will leave some room for forgiveness later IF you both can agree) and you don't want to lose them (which we assume was the reason your wife did what she did...to save the children which may now end up in a broken home with two bitter parents, but that is next weeks debate).
We all agree on those givens?
Now what can be done to correct the problem?