Under the circumstances, I'd very, very strongly say that what they really need is a good family therapist or counsellor with a speciality in divorce and family issues.
Personally, from an ethical and practical viewpoint, I'd say the children should be told, but they should be told *by the person who had the affair*, in an "I messed up and I'm really sorry" sense.
Otherwise, it's really tricky. If the mother tells them about the affair, they may believe she's lying, particularly if the father denies it. Or they may believe it, but feel they have to defend their father, who they still love, to/from a naturally angry and hurt mother, or feel they have to reject him to support her, which can damage the parent child relationships for a long time. If custody issues etc go to the courts or mediation, it may be seen as the mother trying to hurt the father and turn the kids against him.
If they don't say anything, at that age, and in this situation (an affair with another kid's mom) there's a good chance they'll find out on their own, and rightly feel betrayed because they found out via gossip rather than being told by the people they should be able to trust.
I would also add that what's being done with the kids now is kind of cruel. They know very well that something is badly wrong in the marriage, and they are being given a brushoff. When, sometime down the road, they find out their worst fears are being right, they will realize that they were being lied to, which can cause extra anger and resentment on top of the fact that their family has just been destroyed.