It happened at a vehicle wash Sunday night near the 4300 block of West Orem in southwest Houston.
She abandoned two of her daughters - ages 13 and 11 - and then continued to drag her 9-year-old daughter towards a bayou nearby, police said.
Police told the station the mother told the kids before setting the fire that "they were going to see Jesus".
Once officials started to approach the woman, she fled on foot with her children tow. "The older girl tried to escape, but the mother got her back in the auto".More news: Milwaukee taco stand is looking to capitalize on rival's Giannis Antetokounmpo blunder
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Witnesses say the woman's three children - ages 9, 11, and 13 - were all inside the auto when she revved the engine until it caught fire.
A portion of the incident was captured on surveillance camera. The children were unharmed and police haven't said who they are with right now. Police say the woman eventually chose to leave the area with her kids but was captured by Precinct 7 deputy constables.
The mother has been charged with three counts of aggravated assault on a family member. She reportedly tripped and fell.
Houston Fire Department arson investigators were also called to the scene.