So her husband (the dad) is definitely cheating or has before to even suggest to go to the husband first. Most would tell their daughter to protect her. He can easily say oh yes ill stop seeing the other lady. The daughter needs to know now. I'd be pissed if my mother/father did not tell me after doing all this... and there's way to many ads!
This is a double betrayal. They picked their son in law over their daughter....that mother should be ashamed...She doesn't care about her daughter's happiness, just forcing her to keep the family together.
Since it was the dad's idea to not confront the daughter and only confront the husband I would say he is a type that is worried about family image a bit too much. He just doesn't want a divorce in his daughter's feature.
Either way, the risk is also, that the daughter won't believe her parents after confronting her husband and they will be accused of "just trying to get between them", if there is no solid proof of the son in law actually "failing" her - it very much depends on what kind of relationship the parents have with their daughter. It is a hurtful situation all around.