One way of looking at this story is to look at it from the perspective of the two children (who, it should be noted, since these answers refer to them as children: the two are actually fully grown adults. One's a nun and the other is a magistrate).
If you look at the narration in "Dead Woman's Secret," the two are described as very rigidly moralistic, but (as an answer before me has written) their morality lacks compassion. Indeed, the magistrate's execution of the law is described within the narration in almost brutal terms, as a kind of weapon to be wielded against the vulnerable. As for the nun, there's an element of misanthropy informing her seclusion.
When reading their reaction to their discovery, it might be worth noting the degree to which the two might not have actually been transformed by that discovery at all. They've always been judgmental, particularly against any perceived moral infringements. The only real change that has taken place is that now the mother herself has been brought under censure.
I'd suggest that what might make for interesting conversation lies in what this stories says about the son and the daughter and about their own moral inflexibility. What does this story imply about the importance of empathy and compassion, as it relates to standards of virtue or behavior? Can we state, from this story at least, that the later is actually hollow if it is not informed by qualities of the former?