Also shot was Carter Sr.'s daughter-in-law, Amber Carter, who was six months pregnant and was in intensive care in a New Orleans hospital after giving birth to a healthy boy named Aubrey, said her father, Paul Williamson.
Williamson said Carter Sr., 50, had a history of assaulting his wife, Donna Carter, and recently tried to attack her with a machete. Donna Carter had a restraining order against him that her husband had repeatedly violated.
"This had been going on for quite some time," Williamson said. "It was one of those domestic violence things that just gets worse and worse."
A 16-month-old boy was in the house during the shootings but was not hurt. The child was related to the Carters but Rushing was not sure how.
Authorities were called to the home in Holden, about 30 miles east of Baton Rouge, around 10:30 p.m. Saturday. Donna Carter, 49, and Dennis Carter Jr., 26, were dead inside. Found outside were Amber Carter, badly hurt, and their son, 2-year-old Masson Carter, who was dead.
Rushing said it appeared Amber and Masson Carter escaped from a second-floor window but it was not clear if the gunman shot them inside or followed them outside and shot them there. Williamson said his daughter had bullet wounds in her kidney and liver, plus spinal damage sustained when she leapt from the window, probably trying to escape her father-in-law.
Rushing said deputies spotted Dennis Carter Sr. about 20 minutes after the shootings driving on a highway. When they tried to pull him over, he shot and killed himself.
"It's very unusual to have this many victims," Rushing said. "This is an anomaly by any stretch of the imagination."
In a statement released late Sunday, Stephen Alexander, a lawyer representing other family members of Carter Sr., said they were "obviously devastated by their tremendous loss and they ask that the media respect the family's privacy during the grieving process."
All the Carters lived at the house in Holden except Dennis Carter Sr., who used to live there but had recently moved to nearby Hammond. Williamson said Carter Jr. and wife Amber had been planning to move to another house.
Williamson described the senior Carter as a semi-employed mechanic. He said Carter Jr. was a scaffold builder; Amber Carter was a secretary at North Oaks Rehabilitation Center in Hammond, where Donna Carter worked as a data entry clerk.
Rushing said that state police ballistics experts were conducting tests on a gun found in the senior Carter's car.
Williamson said he didn't expect to learn exactly how the killing spree transpired.
"We won't ever know what happened inside that house," he said.