Photos show bullet holes at the scene on Friday.
The mother says her 13-year-old and 15-year-old children were riding in a golf cart with three other friends.
A black SUV drove up to the teens near Bees Creek and Sienna Parkway and someone inside fired shots, Fort Bend County sheriff's deputies say.
The teens got away unharmed. The family believes the shooting was random.
Deputies say there is no further suspect or vehicle description as there were no cameras located in the area of the shooting.
RELATED: At a glance: Road rage attacks against children in the Houston area
Road rage shooting critically injures 9-year-old girl