The incident happened Thursday around 9:30 p.m. in the 1800 block of W. Mount Houston Road.
Authorities say the father got into some sort of argument with the suspect. That suspect pulled out a gun, and the father tried to drive off.
The gunman shot at the car, which set off fireworks in the vehicle, causing it to catch fire, deputies say.
"Family had bought fireworks. It is believed gunfire struck the fireworks causing them to ignite," Harris County Sheriff Ed Gonzalez said.
Dramatic video shows flames overtaking the car.
The two children, a 1-year-old and 2-years-old, suffered extensive burns and are in critical condition.
HCFMO investigators are on a scene involving a vehicle fire that occurred after a road rage shooting incident. 2 children and 2 adults were burned. Burns occurred when fireworks inside the car went off due to the gun shots. More info when available. #hounews pic.twitter.com/4RGxZiTK1M— Harris Co. FMO (@hcfmo) July 5, 2019
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 suspect and that vehicle, but Sheriff Gonzalez said that the shooter appeared to be with the family earlier in the night.