Robyn McHale, 28, died six days after being airlifted to Royal London Hospital in a critical condition from outside Forres Primary School in Hoddesdon, Hertfordshire.
An inquest into her death heard how just moments before the collision in February last year, she had been involved in a heated argument at the school gates.
Ms McHale was heard shouting "you f****** grass" before running towards another mum, Tara Jarmin, with her arms flailing and starting a tussle.
The inquest heard she had blamed the other mum after headteacher Sue Camp called the single mum-of-three into a meeting to discuss child car issues.
Robyn, from Hoddesdon, was said to have become "upset and angry" before storming out of the school and confronting the woman.
"Not long after, Tara Jarmin ran to me very agitated and in shock. She said something about Ms McHale and a car so I went outside with a first aid kit. That was when I saw her lying on the road unconscious and bleeding from a head wound."
Hatfield coroner Geoffrey Sullivan was told after reaching the woman, Robyn slipped from the kerb into the road and her head was struck by the rear near side wheel of a passing transit type van causing a massive head injury.
The inquest was told that initially police arrested the woman Robyn had run up to as well as a 15 year old girl.
But after officers were able to view CCTV footage which captured the incident, no charges were brought against them.
Police constable Ian Marsh confirmed that the van which struck mother-of-three Robyn had been travelling at just 21mph and had stopped immediately after the incident.
The woman said she heard a loud bang and realised that van had struck Robyn.
She told officers "It was a freak accident."
In a tribute Robyn's sister Alexander McHale said: "The family and friends are all devastated by Robyn's death and miss her very much. She had a cast iron exterior but a soft interior and gave her all to her three children. She touched the hearts of everyone she knew."
The coroner recorded a verdict of accidental death.