TAMPA, Fla.—A woman serving two life terms for killing her teenage children in 2011 while her husband was deployed overseas is seeking a new trial. A Tampa jury rejected the insanity defense for Julie Schenecker, 61, and convicted her in the shooting deaths of her 16-year-old daughter Calyx and 13-year-old son Beau. Schenecker is seeking a new trial in an appeal she filed herself, the Tampa Bay Times reported. She contends that the public defenders who represented her were ineffective. She argues that they should have sought to move the trial away from Tampa because of extensive local news coverage and that they didn’t call certain witnesses who could have bolstered her insanity claim. State prosecutors said a hearing is necessary to address some of the 20 claims she made. Judge Michelle Sisco ordered that Schenecker return to court for the March 10 hearing with a new attorney appointed to …