Two of the children left the vehicle's path, but Staggs 3-year-old was beaten, Ogg's office said in the release.
The child was first caught under the right-hand tire of the SUV, the release said. Stagg did not stop immediately and the toddler was hit again by the vehicle's rear tire – which, according to the press release, weighs about 5,600 pounds.
Stagg initially told the police that she believed she had hit a braking threshold, Release said.
The incident occurred on June 11, and Stagg was arrested on Thursday and charged with negligent murder, prosecutors said. If convicted, she faces up to 10 years in prison.
An attorney for Stagg was not immediately available.
According to CNN member KTRK, Stagg removed two older children from child protection services in 2013. After the death of 3-year-old Lord Renfro, her two surviving children were also removed, the station reported.
"Every parent is required to protect their children, even from themselves," said Ogg. "Cars are not toys and playing chickens with your kids is not a game."