I’d be surprised if she managed to not let her kids find out.
Infidelity causes a version of PTSD, PISD. The trauma is very similar to a death. The shock, hurt, confusion would cause a normal person, who loves their partner, to react. This may be rage, crying, disbelief, anger or shock. But it’s usual to react to a trauma and if the op got angry or sad then that is normal.
I reacted in a similar way when my grandmother died - I knew it was coming (she was in her mid 90s), but I was shocked and I cried non stop all day. I could not have hidden it from my children.
Her cheating loser husband who has caused this mess is to blame for the children’s upset. He should have had the integrity and morals not to betray his own vows. And had the guts to allow his wife an insight into his lies and deceit at a time when it was appropriate, maybe allowing her to join the happy party of extra marital activity that he was indulging in. But no he is a selfish man who wanted wifey to remain faithful while he (No doubt) lied to two women.
Does her husband really know?
Personally I’d contact the other persons husband and find out what he knows. For all you know your husband is lying. Your husband is a liar at the end of day, he has reduced ethics and morals - his word can’t be taken as true. He may not want you to contact the other husband to stop you blowing up the OW world or affecting her kids etc. He may have lied to her about things too. He may have other plans which they are hiding and it’s crucial her husband doesn’t know. They may have no intention of leaving so dont want him to know. It may have been going in for years and he may be a technical whizz who can read all their emails/texts. She may have told him he’s just a best mate. So the first thing I would do is call that husband, apologise for the intrusion and find out exactly what he knows.