IMHO, lying to your kids or covering up the truth is a sure fire way to "diminish" the love, respect, affection etc that they have for YOU. How can a court ask you to do that?
XWH had similar verbage in his divorce decree with his kids mother. His interpretation was that it meant no saying things like "Mommy and Daddy divorced because you were bad" or "Daddy left because you were bad and he doesn't love you anymore". "You have to pick who you want to love, Mom or Dad." etc... stuff like that.
The truth is the truth, and that includes his affair. Answering the kids honestly but in a way that is appropriate for their age is enough in my opinion.
As someone somewhere on here said...He fired you as his wife. It is no longer your job to protect him and his secrets.
The kids will find out the whole truth as they get older... you don't want them to feel you were dishonest or kept something from them.
Best of luck... I don't envy you the position you're in.
((hugs!))Me: Looking forward to the future
Him: Left behind in the past
Rock bottom became the solid foundation on which I rebuilt my life. ~ JK Rowling