Analyze the deaths of the three children. What is the function of this tragedy in the overall structure of the book?

I think the death of the three children functions as a framing to overall tragedy that this story is. Both Jude and Sue are finally characterized by their responses to the tragedy.

Hardy emphasizes the contrast between Jude and Sue’s reactions to their children’s deaths by relating their long arguments in the days after the event. Although he was the more demonstrative partner in their relationship, Jude is much calmer than Sue in the face of crisis - while she sleeps or has hysterics, he makes practical arrangements to bury the children, and he is the first to accept that a doctor will be no help in reviving them.

In contrast, Sue is so distraught that she has a miscarriage. Hardy heavily insinuates that Sue’s sudden turn to religious conservatism is inspired by her recent personal trauma; the Widow Edlin even speculates out loud that this might be the case. Hardy has hinted throughout the novel that Sue’s personality might change drastically in a time of crisis; even in benign situations, she is characterized as anxious and high-strung. Her turn to religious conservatism, then, could be read as a criticism of fervent religiosity in general; Hardy seems to suggest that strict Christian doctrine is something that emotionally vulnerable people turn to in times of crisis, and is therefore not to be taken seriously.