Scorpius and Albus Cause a Death Attempting to Save A Life
Albus and Scorpius have their own personal motivations for their adventure in time, but they are motivated by the possibility of saving the life of innocent Cedric Diggory. By teaming up with Delphi, whose motivations they assume to be pure, the boys assume that they will ultimately save Cedric's life with no repercussions. The fact that their alliance with Delphi to save Cedric directly results in the death of Craig Bowker Jr. is an example of situational irony; the purpose of their journey is to save a "spare," and it results in the death of another. The death leads to Harry and Albus bonding over the guilt of being responsible for the death of an innocent classmate.
Harry and Delphi as Orphans
Harry Potter is an orphan, raised by his aunt and uncle Petunia and Vernon Dursley. He was unwanted in their home, and lived there only for the magical protection their custody offered. Delphi is an orphan as well, and she was also unwanted by her legal guardian Euphemia Rowle, who only took care of Delphi because she was being paid to do so. Though they are both unwanted orphans whose greatest desire is to know their parents, Harry and Delphi end up on different paths. Harry had people to show him from right and wrong, while Delphi didn't. Harry had the luxury of being adopted by his family at Hogwarts—his friends, his instructors—but Delphi ultimately did not. The irony that Harry caused Delphi to be an orphan, and the father she wishes to meet caused Harry to be one, adds extra tension to their final confrontation.
Harry Isolating Albus from Scorpius
Harry was more than sure that Scorpius was the reason why Lord Voldemort was rising again. As a result, he decided to separate Albus from his only friend at Hogwarts. Since Harry spent his energy trying to separate his son from Scorpius, he didn't notice his own part in his son's unhappiness. When he asked Bane about his son, he told him that he was surrounded by a "black cloud." Though Harry interpreted that to mean Scorpius Malfoy, it turns out to be Albus' own isolation—caused by Harry's fear of Scorpius. This example of dramatic irony allows the reader to see that Harry's good intentions result in tragic effects. Since we know that Scorpius is a good influence on Albus, Harry's actions end up having the opposite effect from the one intended.
Voldemort's Child
The crux of the plot is the rumor that Voldemort has fathered a son and that Scorpius is that son. This causes Scorpius to become an outcast which indirectly leads to his alliance with Delphi. This also causes Harry to be suspicious of Scorpius, and ultimately leads to conflict between Draco and Harry as well as Albus and Harry. The rumor is partly true: Voldemort does have a child. But it is not Scorpius, and not a boy. The situational irony is that while Scorpius has suffered from the rumors of being Voldemort's child, the child of Voldemort has been in his midst the whole time.