The maximum force that even the torquiest motor could apply to the door would be limited by the coefficient of static friction of the rear driving wheels. At some point, they would start skidding.
So if we know the weight of the ECV + rider + child as 500 pounds and using 0.79 as the coefficient of friction of synthetic rubber on cut pile carpet*, we can estimate that the maximum torque that could be applied by the motor onto the door as 400 pounds of force or 1800 newtons. As per the estimate in the other thread, the impact of the ECV going from 5 mph to a full stop in 100 milliseconds is about 5000 newtons.
It's not insignificant, but I'd still go with the impact force as being the primary cause of the shearing force on the door hinge.
Also note that this motor would need about 360 Nm of torque to achieve 1800 newtons of force on the door. This is about double the torque of a 3000 watt motor I found referenced in a 50 mph racing scooter being discussed over in the electric scooter forums. 110 Nm was a more reasonable figure for a 2000 watt motor quoted which would give us 550 newtons of force on the door. OTOH, I'm not an expert in ECV design so ECVs may use gearing to increase available torque while reducing top speed, which would make sense. That would take us back up to 1800 newtons.
* This coefficient of friction is off of some paper I found on the slipping force of shoes on carpet. https://www.jstage.jst.go.jp/article/jte2000/47/2/47_2_53/_pdf
African or European ECV?