It mounted the pavement and rammed into Poppy and 17-month-old Taylor, who was in a pram.
The distraught mother can be seen scrambling to the aid of Poppy, who was trapped under the front of the vehicle.
She said the accident happened when the Toyata was sent outof control at 30mph when it was clipped by a Vauxhall Corsa.
The mother-of-four said: "A white Vauxhall Corsa went straight through the junction of The Avenue and Seymour Road instead of giving way. The lines are so faint that they are barely visible.
"It clipped the back of a silver Toyota Yaris which forced that car to spin 90 degrees and mount the pavement.
"The car hit us and pinned me, my Taylor who was in a pram, and my five-year-old daughter Poppy up against a fence.
"I remember lying on the floor and my five-year-old was laying right next to me with the car over her legs.
"We were all screaming because the car was still revving and I thought that car was going to crush my children. I don't remember how we got out. We're lucky to be alive."
White feared her children would be crushed as they were trapped between the car and the fence.
The family was rushed to hospital with White being treated for a facial injury and Poppy treated for leg injuries.
Luckily the young girls avoided long term injuries though White has suffered whiplash and says she is "really hurting at the moment".
White said the mental scars of the incident are taking a toll.
She has been left traumatised by the ordeal as has her eldest daughter Ellie, 11, who witnessed the incident.
She added: "To move on from this I need answers. The thought of walking my kids to school gives me such anxiety at the moment.
"My heart is pounding just speaking about it.
"If it hadn't been a fence and it was a brick wall I think Poppy certainly wouldn't be here now.
"I really thought I was going to lose them [my two younger daughters] that day. I just keep reliving it in my head.
"We really were very lucky. We really don't want to be apart from each other at the moment."
Lee Scarisbrick, 58, who lives on the junction in Benfleet, Essex, caught the crash on his CCTV camera.
Scarisbrick said: "It's harrowing to watch. You can't quite believe how Mandy and her children weren't killed.
"The lady driving the car that was clipped was absolutely traumatised because she thought she could have killed them.
"This junction has seen many accidents over the last 30 years that I've lived here. On the same day I saw three other vehicles overshoot the junction.
"I first reported it to the council in 2015 but they say the lines do not meet the requirement for repainting. It's going to take a fatality before they do anything."
He and Mandy have both urged Essex County Council to repaint the give way markings.
Essex Highways has responded to the issue.
A spokesperson said: "Our inspectors will visit and check the lines and repaint if required.
However, there are also prominent 'Give Way' signs on posts at the junction."
