When they arrived at the apartment complex on the 7200 block of Gramercy Place, they found Dixon on a second floor balcony waving a handgun and yelling out at officers to shoot her.
Officers were able to arrest her.
Inside the apartment they found 5-year-old Christian and 1-year-old Michael Jr. clinging to life.
The family and the community are trying to deal with this terrible tragedy.
"To me she seemed like she was a good mother," said Ayanna Faulcon, the cousin of the children's father. "She kept her kids clean, she'd take her kids to different functions, she'd go out and play with them. I never knew there was anything wrong."
Faulcon also said the mother had a care-giver.
Civil rights groups in the community are asking the Board of Supervisors and Child Protective Services to take account of what went wrong.