It is indeed your choice on what you tell your children. It is doing them no service in keeping this from them. Their father is having an affair. He is leaving to pursue the affair. That is the truth. He isn’t leaving because Mommy and Daddy aren’t getting along.
I know that it might seem mean to tell them the real reason that their life is being shattered (I used to too). But it isn't. Some physiologists do indeed recommend informing the children about a spouse’s affair. Dr. Williard Harley comes to mind. In fact he thinks it is beyond cruel to keep this information from them. Their Dad’s choices to violate his marriage will affect these kids for a very long time. I, and quite a few professionals, think that kids need to be shown that it isn’t ok to violate one’s wedding vows.
But regardless, I wish you well.
Congratulations on standing up to your MIL! Your husband should take them to see his mother. You have other things to worry about now. Like your livelihood.
I'm a man . . . But I can change . . . If I have to . . . I guess . . .