But she later confessed she had found the children playing in the auto, parked outside their house, and when her daughter refused to exit she shut the door to teach her a lesson.
She says she thought they'd be able to get themselves out, so she went back to inside to smoke weed and fell asleep for hours.
Randolph has been booked into the Parker Country Jail. When they refused to get out, she closed the door to "teach them a lesson". They arrived on the scene, located west of Lake Weatherford at approximately 4 p.m.
The pair were pronounced dead from suspected extreme heat exposure and the manner of death in each child is pending, according to the Telegram.
Authorities were alerted to the incident just after 4 p.m., a news release said, when the temperature outside had reached 96 degrees.
On Friday, the Texas Rangers and a Dallas-based senior federal special agent conducted a final interview with Randolph, where she implicated herself in her children's deaths.
She said she realized the children were missing after about a half hour of silence and discovered them unresponsive inside the auto.
Authorities said Randolph initially told officers that she had been folding laundry in the house while her children played outside.
But on Friday, the story changed.
She called police, saying she found the children unresponsive. Of those, three have been in North Texas, including the two Friday in Parker County. The Tarrant County medical examiner's office has not yet ruled on the manner and cause of each child's death. A bond has not been set, and we don't know whether or not she's hired an attorney. The investigators involved in the case believe Randolph was exclusively responsible for the death of her two children. When she realized they had both died, she phoned the police.