Sue Duke, 41, was crushed between daughter Lauren's Ford Ka and another vehicle as she tried to guide her daughter back into a parking space.
It is thought the car suddenly lurched backwards as Mrs Duke instructed Lauren on how to reverse into a space.
Mrs Duke was airlifted to hospital with head injuries after the accident in Rochester, Kent.
Her brother-in-law Malcolm Mitchell told reporters that he thought Lauren might have mixed up the brake pedal and the accelerator. He said: "She seemed to be practising reversing. We think Susan got out to direct her. She must have got the brake pedal and the accelerator pedal mixed up and pressed the wrong one."
What a terrible story. Our sympathies to the family.