Randolph said she searched the premises for about another half an hour before she found them unconscious inside her locked vehicle, which was parked out on their driveway.
She has been charged with two first-degree felony counts of injury to a child causing serious bodily injury.
The incident happened in late May, when she initially told police the children locked themselves inside the vehicle.
Randolph initially told authorities she was folding laundry and watching TV and realized within an hour that her kids were "gone".
Randolph told the police she was trying to teach the 2-year-old a lesson by locking her in the vehicle with her brother. The temperature was reported to reach 96 degrees on May 26.
According to police statements, Randolph broke the window before police arrived to make the deaths look like an accident.
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The toddlers died in the auto.
The children were pronounced dead at around 16:30, which was four hours after they had been left in the vehicle.
She then told officers that she had to break a window and rescue the children, then called 911, authorities said. "The defendant said she was asleep for two or three hours".
The state of Texas has had 121 heat-related deaths of young children left in vehicles since 1990, more than any other USA state, according to KidAndCars.org and Star-Telegram researchers. According to the data, an average of 37 children die in hot cars annually in the United States.
At the time Randolph stated the kids were exposed to the extreme temperature levels in the auto for "no greater than an hour".
But she eventually admitted that she had found children playing in the auto at about 12:15 on that day. No bond was set for the woman at last report.