Chicago police caught up with the 19-year-old suspect at Sunnyside and Laramie after the car crashed into a house. Travis Golden of Chicago has been charged in the incident.
Police said it appears the kidnapping was unintentional.
The children are 1 and 6 years old. They were not hurt.
The children's family says this ordeal began when an unidentified man first tried to rob one of the children's other relatives, then decided to steal their mother's car.
Tiny Gunn, 24, says as she pulled into the alley behind her family's home and saw her cousin talking to a man she didn't know. It turns out the man was allegedly trying to steal a diamond earring. Gunn didn't realize that she had interrupted a robbery attempt. She got out of the car and asked her cousin to park the vehicle when Golden allegedly got in the driver's seat.
The family called 911 as they gave pursuit. Police eventually joined the chase.
"Chasing the car down, and we hear gunshots," Gunn said. "I'm thinking about my kids. My kids is dead, my kids, my cousin is dead. That's the only thing that kept going through my mind was they were dead. And then the police, the police came and they said they got him, they got him, and all I'm thinking, my kids. Where's my kids? I just want my kids."
Jerome, the 6-year-old, said he had a bruise on his left leg. His younger sister, Tarrah, was not hurt.