I've seen good arguments here for telling them and not telling them.
Cole said some very wise words, though. If I were in your shoes, I wouldn't do it and wait, for the same reasons.
But that's easy to say, from this distance. You are the only one who can know how your sons will presumably react.
One thing to add; if you are going to tell them, do it together with your wife. Let them see inmmediately that you both sorted it out, that they immediately can see that things are good between you and that there still will be a loving, caring and solid family.
Because there is, I can see in what you are telling here.
Respect. For both of you. And your boys.
Wish you good luck with this situation. But you all will manage, I'm sure of that.