The report said Fuentes was unemployed and had been living in the SUV with his sons before the tragedy.
Fuentes had become depressed after their mother died of a brain aneurysm in 2008, according to The Los Angeles Times,
The publication reported that the Los Angeles County Department of Children and Family Services received anonymous calls that accused Fuentes of abusing the boys.
The officials were only able to verify one accusation, a 2010 incident in which Fuentes beat his then-5-year-old son with a belt before they were placed on supervision for a year.
Jail records show that Fuentes is currently held at the Twin Towers Correctional Facility, awaiting transfer to a state prison.