ST. AUGUSTINE, FLA. — Michelle O’Connell, 24, the doting mother of a 4-year-old girl, was dying from a gunshot in the mouth. Next to her was a semiautomatic pistol that belonged to her boyfriend, Jeremy Banks, a deputy sheriff for St. Johns County. A second bullet had burrowed into the carpet by her right arm. Ms. Maynard quickly escorted Mr. Banks, who had been drinking, out of the house. “All of a sudden he started growling like an animal,” she said. With his fists, Mr. Banks pounded dents in a police car.... Within minutes of the shooting on Sept. 2,...