Sgt. Alfredo Reyes tells the Los Angeles Times that the children were found in a red van that was spotted on a Los Angeles freeway around 10:30 a.m. Wednesday.
KABC-TV showed the mother being handcuffed and the children and a dog being removed from the van.
Reyes says 11-year-old Michelle Hogan, her 4-year-old brother, Jonathan, and 3-year-old sister, Jasmine, were taken to a police station for questioning along with 28-year-old Carolyn Hogan.
The family had driven from Greensboro, Ga., and vanished Tuesday morning after leaving a mission in Los Angeles' Skid Row.
A Georgia court had issued a protective order for the children