The incident happened Thursday around 9:30 p.m.
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Authorities said the father got into some sort of argument with a person who pulled out a gun.
Officials said the father tried to drive off but the gunman shot at the car, which set off fireworks in the vehicle, causing it to catch fire.
"It is believed gunfire struck the fireworks causing them to ignite," Harris County Sheriff Ed Gonzalez said.
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The two children, a 1-year-old and 2-years-old, suffered extensive burns and are in critical condition. The condition of their parents is unknown.
Investigators said some good Samaritans came to the rescue to help the family to an ER clinic.
The shooter took off in a newer model Ford Expedition with possibly a woman and two other people.
There is no description of the shooter, but Sheriff Gonzalez said that the shooter appeared to be with the family earlier in the night.