Are Madame Defarge's actions just?

I think we can all agree that Madame Defarge's anger is a justifiable emotion. After all, her sister was raped by the Evremonde brothers, and her brother was killed for trying to defend the victim. Toward the end of Book Three, Madame Defarge reveals that many of her family members died as a result of the Evremonde brothers' cruelties.
However, Madame Defarge's anger spirals into uncontrollable rage, and she begins to rely on acts of vengeance to soothe her emotional pain. When Lucie begs for mercy for Charles, Madame Defarge refuses her. She is content to punish the innocent for the sins of the guilty.

“As a wife and mother,” cried Lucie, most earnestly, “I implore you to have pity on me and not to exercise any power that you possess, against my innocent husband, but to use it in his behalf. O sister-woman, think of me. As a wife and mother!”
Madame Defarge looked, coldly as ever, at the suppliant, and said, turning to her friend The Vengeance:
“The wives and mothers we have been used to see, since we were as little as this child, and much less, have not been greatly considered. . . . All our lives, we have seen our sister-women suffer, in themselves and in their children, poverty, nakedness, hunger, thirst, sickness, misery, oppression and neglect of all kinds.”
“We have borne this a long time,” said Madame Defarge, turning her eyes again upon Lucie. “Judge you! Is it likely that the trouble of one wife and mother would be much to us now?"

Later in the book, we discover the reasons for Madame Defarge's hard-heartedness and how suffering caused this characteristic to be embedded in her soul. While others may have been refined by suffering, pain produces nothing but inveterate rage, hatred, and vindictiveness in Madame Defarge. At this point, her anger has robbed her of her humanity.

But, imbued from her childhood with a brooding sense of wrong, and an inveterate hatred of a class, opportunity had developed her into a tigress. She was absolutely without pity. If she had ever had the virtue in her, it had quite gone out of her.
It was nothing to her, that an innocent man was to die for the sins of his forefathers; she saw, not him, but them. It was nothing to her, that his wife was to be made a widow and his daughter an orphan; that was insufficient punishment, because they were her natural enemies and her prey, and as such had no right to live.

Although Madame Defarge has good reason to be angry, it can be argued that her actions in tormenting the innocent are morally reprehensible. We can see, however, that Madame Defarge is a broken woman by the end of the novel. She is said to have no pity for herself or others. As Charles's supposed execution nears, she marches toward Lucie's dwelling. There, she tries to kill Lucie but is thwarted by Miss Pross. The Englishwoman struggles with Madame Defarge, and in the ensuing struggle, the latter's gun goes off.
Madame Defarge dies as a result. It can be argued that death is a fitting end for one whose hatred has so tormented the innocent.