I suggest you tell them the truth -- that their relationship, in your opinion, was the not the only problem in your marriage to their mother, but you DO believe it is the major obstacle to her wanting to WORK on the marriage, and that that's very typical, from what you've learned. That you love her, didn't want a divorce, but you also weren't willing to remain married if she refused to give up her boyfriend. That you love them, this was NOT their fault, and that you have never lied to them and never will, and that they can always come to you and ask you ANYTHING, and you'll be truthful with them.
That you love their mother, and this doesn't make her a horrible person, but it WAS a horrible choice she made, and that you're no longer willing to lie about it to cover it up.
