The fire started in the vehicle parked on the driveway and spread to the house in Ashby-de-la-Zouch, at about 05:00 GMT on 5 December.
Carly Chambers, 25, said she was terrified for her children's safety as there was "explosion after explosion".
The fire service is investigating, but police are treating it as suspicious.
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Ms Chambers was asleep in the house with her two-year-old son and daughter, six, when she was woken by her stepfather "screaming 'fire, fire, get the kids, get out of the house'".
"The children were scared, there was explosion after explosion, it was really frightening, they wouldn't stop crying," she said.
"We got to the bottom of the stairs the door exploded at us - we got covered in glass - we just had to run."
Ms Chambers believes it was a deliberate attack, but has "no idea who would want to do this, especially to a house where young children are".
"My two innocent children's lives could have been taken by some stupid act," she said.
Ms Chambers added that she "still feels distraught", but was thankful for the help and support from the community.
Leicestershire Police said: "The fire is being treated as suspicious.
"Due to the high winds the flames caused some damage to a van and the front door of the property."
Police would like to speak to anyone who may have witnessed the incident or has any information about the fire to contact them.
A mother-of-two had "seconds to escape" from their Leicestershire home after it caught fire during a suspected arson attack on their car.