PITTSBURGH -- A woman accused of drowning her two young sons in a bathtub had tried to kill the boys before by leaving one in a hot vehicle and by running over both with her van while they were tied up with twine, a prosecutor said Wednesday.

Laurel Schlemmer is charged with killing 6-year-old Daniel and 3-year-old Luke in April 2014 so she could focus on raising their older brother, who was then 7. Prosecutors at Schlemmer’s bench trial are seeking a first-degree murder conviction, which carries life in prison.

Laurel Schlemmer CBS Pittsburgh

After walking the eldest boy to a school bus stop, Schlemmer walked back to her house planning how she’d kill his brothers that day because she was “fixated that Daniel and Luke were not normal children” - even though they were - and that she’d be a better mother if the younger boys were “in heaven,” Allegheny County Assistant District Attorney Lisa Pellegrino told the judge in her opening statement.

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Schlemmer’s attorney, Michael Machen, didn’t make an opening statement. But in a pretrial discussion with the judge, he made it clear that he’ll try to prove Schlemmer was insane or operating under diminished mental capacity.

Schlemmer, 43, was sworn in, suggesting Machen plans to call her as a witness. The attorneys are under a gag order and can’t speak about the trial or their strategy outside the courtroom.

But Pellegrini told the judge evidence of the past attempts on Daniel’s and Luke’s lives - and other evidence from the drowning scene - will prove Schlemmer planned their deaths.

Among other things, Pellegrini played a recording of a 911 call in which Schlemmer told a dispatcher she had let the boys play in the bathtub while she “went to the restroom and took longer than I should have or planned and, when I came back, they were unconscious.”

McCandless Township Officer Todd Ray testified that the boys had been dried off and were lying next to each other by the time he arrived. Only their hair was damp, and it appeared to have been combed, he testified.

Schlemmer, meanwhile, had changed into dry clothes before calling 911, Pellegrini said.

Pellegrini contends Schlemmer had put each boy face-down in the tub, then sat on them until they were unresponsive. Luke died that day and Daniel died four days later. The medical examiner ruled both drowned.

Their father, Mark, was at work at the time. He sat in the courtroom, sometime hunched over, his eyes red. He shook his head when Schlemmer said she understood her rights and had been found mentally competent to stand trial after several stints in a state hospital.

Ross Township Officer Michael Thomas testified he was called to a mall lot in September 2009 after security workers found Daniel in a parked vehicle. Thomas used a heat sensor to determine the vehicle was 112 degrees inside and said the boy had been inside about 20 minutes. He also said, however, that the front windows were open about 6 inches each and that he was able to reach inside to unlock a door.

Schlemmer was ticketed for leaving Daniel alone in the car.

Other witnesses testified to an April 2013 incident at Schlemmer’s parents’ house, where she backed her van over Daniel and Luke.

Police and a hospital nurse said the boys had tire tracks on their abdomens. The boys were treated for various broken bones, but police and county child welfare caseworkers never determined exactly how and why the boys were run over.