Personally I find it very strange and unhealthy to continue other people’s secrets, and enable the lie. Lie’s are usually propped up by other people. Very few people are so discreet that no-one notices.
And then the person who has been lied to, also then has that horrible feeling that others may well have known, but she didn’t. It doesn’t get much more humiliating than that.
Have no doubt, cheating is about power. The power to do what you like, and not give the other person the choice to do the same or leave. Often, it can be part of other emotional abuse that is going on, manipulation, and other lies such as over money. The sooner it is exposed - then the sooner that the power they have is diminished. Remembering that MIL has probably been worrying about her own sanity for years, being gas lit, ‘is he really at the meeting?’ She might think. Of course he must be, I’ve just become too untrusting… she is not in a good place. Whatever it might seem on the outside. No one who is being cheated on and still doesn’t know it, is in a good place in the relationship.
Tell her, either through your DH or direct, but tell her. Tell her respectfully. And she will know that someone respects her, someone cares about her. What she does with that information is up to her.