The shooting happened Wednesday afternoon in the parking lot of Ramona Preschool.
Deputies said the mother and her three kids were sitting in a Honda when her son, who is under the age of 5, got a hold of the shotgun. That mother was rushed to the hospital and is listed in stable condition.
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The Los Angeles County Sheriff's Department said Thursday that a man was arrested that same day on various felonies, including a warrant, criminal storage of a firearm and child endangerment.
It is not clear how that man is connected to the woman.
Four children are now in custody of the L.A. County Department of Children and Family Services.