The Angelina County Sheriff's Office says an 8-year-old and 3-year-old died after the tree hit the back of the vehicle in Lufkin, about 115 miles (185 kilometers) northeast of Houston.
Monroe County Coroner Alan Gurley says multiple people were injured and multiple homes were damaged in Hamilton, Mississippi, which is 140 miles (225 kilometers) southwest of Memphis, Tennessee.
Almost 90,000 customers were without electricity in Texas, Mississippi, Louisiana, Arkansas, and Georgia as of midday Sunday, according to www.poweroutage.us as the severe weather left a trail of destruction.
The storm system's death toll rose to at least five on Sunday, when authorities reported the death of a Texas woman whose mobile home was destroyed Saturday night.
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A preliminary damage survey showed an EF-3 tornado, with winds up to 140 miles per hour, touched down in Robertson County, the NWS in Fort Worth said.
The roof of a hotel in New Albany, Mississippi, was damaged, although the cause was unclear. Capt. Alton Lenderman said the parents, who were in the front seats, were not injured.
Two people were hospitalized for injuries not thought to be life-threatening, while others were treated at the scene for minor injuries, Yezak said. Heavy rain may also lead to localized flash flooding in areas prone to flooding. Some people had to be extricated from their homes.
Meantime a 13-year-old boy drowned in a drainage area in West Monroe, Louisiana, late Saturday afternoon, according to the Ouachita Parish Sheriff's Office.
He said the threat for severe weather is greatest at such times but that the risk remained even after warm temperatures dropped.