Randolph initially told police the children, 1-year old Cavanaugh Ramirez and 2-year old Juliet Ramirez, had locked themselves in the auto. According to NBC Dallas-Fort Worth, temperatures reached 96 degrees that day.
Randolph faces two first-degree felony counts of injury to a child causing serious bodily injury.
She called police, saying she found the children unresponsive.
Deputies said the mother then went inside her home, smoked marijuana and fell asleep for several hours. Her bond has not been set. She claimed they were in the auto for no more than an hour.
The group advises parents to put something they will need by their child's vehicle seat - a purse, wallet or phone, for example - as an additional reminder to check the back.
According to the Parker County Sheriff's Office, when asked how long the children might have been exposed to the high temperatures inside the auto, Randolph responded immediately: "No more than an hour".
At the time, the news release said, Randolph told police the children were playing in an enclosed back porch when she realized they were "gone".
At the time, Randolph said the kids were exposed to the extreme temperatures in the vehicle for "no more than an hour". After she found both children unresponsive, Randolph claimed she broke a window of the vehicle to gain entry in an attempt to save the children.
Randolph was booked into the Parker County Jail.
The children were identified as a 16 month-old boy and a 2-year-old girl.
Around 4:30 p.m., medical responders who had arrived pronounced her children dead. The Parker County Sheriff's Department determined that Randolph changing her story about how her children died was probable cause for arrest. This bill requires all new cars to come equipped with a device that alerts the owner of the vehicle if the child is left behind after the auto is shut off.
When detectives were first called to the home west of Lake Weatherford on May 26, Randolph spun a different tale.
Fowler said that any incidents involving any child are hard ones, but this call was especially heartbreaking because of the unfortunate deaths of the two children.