Four people total were inside the trailer, with three suffering burn injuries -- a mother and two children.
The burn victims were flown by medical helicopter to Parkland Hospital's burn unit.
The mother, 21, has been identified to FOX 4 as Angelica Calhoun by her father.
Calhoun and her 3-year-old child had burns on their arms and smoke injuries.
A 2-year-old child suffered burns to the face, neck and arms.
Calhoun's boyfriend, 41-year-old Michael Wooten, was also inside when the fire sparked, according to Calhoun's father.
Wooten reportedly sustained some cuts and helped Calhoun get the kids out through a back window.
The fire marshal said the fire started about 3 p.m. and may have been the result of an electrical short.