Randolph told the police her children had been inside the auto "no more than an hour".
A Parker County mother who told investigators that she locked her two children in a hot vehicle as punishment was arrested Friday, authorities said.
But Randolph later admitted to authorities that she left the kids in the vehicle.
Randolph said she went back into the house, smoked marijuana and took a nap for two or three hours, the complaint states.
However, investigators said Randolph in subsequent interviews "created several variations of the events which lead to the death of her children", and in an interview on Friday she implicated herself.
The pair were pronounced dead around half-an-hour after authorities were notified.
Randolph found her two children, a 16-month-old boy named Cavanaugh Ramirez and 2-year-old Juliet Ramirez, playing inside the vehicle. She said about 20 to 30 minutes had passed when she realized her kids were "gone". She later told investigators that she later broke the vehicle window to make it look like an accident.
Randolph was booked into the Parker County Jail.
She has been jailed and no bail has been set.
Cynthia Marie Randolph, 25, told investigators with the Parker County Sheriff's Office that she was trying to teach her 2-year-old daughter a lesson by putting in the vehicle with her 16-month-old brother.
She said she then broke the auto window to corroborate her initial story.
At first, authorities say that the suspect told them that she was folding laundry while her children were outside playing.
The Texas mom is now in custody at Park County Jail. Chief Jeff Gibson said they are not calling Kaytlynn's case a murder investigation because the medical examiner has not released an official cause of death.
On that day, it was aobut 96 degrees in the area, according to the Dallas Morning News.