Yet such extreme violence rarely comes out of the blue, and since the killings, fragments of information have surfaced that hint that the family’s veneer may have covered a more turbulent reality. Ms. Schenecker was involved in a traffic accident in November, her Mercedes rear-ending a trailer being towed by another car. Florida Highway Patrol troopers noted that she showed “signs of drug impairment,” including “dilated pupils” and “mush-mouthed speech.” But she was discharged from the hospital before blood could be drawn, according to the troopers’ report.

Two days later, police detectives were sent to the Schenecker house after Calyx told a counselor that her mother had slapped her in the face. Ms. Schenecker did not dispute that she had hit her daughter, but she said that Calyx had called her “disgusting” and told her, “You’re not my parent.” The detectives concluded that “there is no evidence of a criminal offense in this case.”

Others also noticed small things that at the time seemed insignificant, but now make them wonder. Mr. Bingham, the track and field coach, recalled that sometime in the fall, Calyx’s father told him that arrangements would have to be made to pick her up after practice because his wife was undergoing “rehab.” Mr. Bingham did not inquire about the treatment. “It wasn’t my job to ask, as a coach,” he said.

Lisa Pilch, who played Division 1 volleyball with Julie Schenecker at the University of Northern Iowa and kept in touch over the years, noticed at a reunion in 2009 that something seemed different about her college friend. “I just thought that she was a little subdued,” Ms. Pilch said. “I thought her eyes looked a little bit either distant or vacant.”

Forensic researchers who have studied mothers convicted of killing their children said that such women often leave a trail of clues behind them. “In almost every case there’s obvious signs,” said Cheryl L. Meyer, a professor at Wright State University whose research team examined 219 cases of maternal filicide and conducted lengthy interviews with 40 of the mothers.