A crew from nearby Grindon Fire Station pushed back the car and they and paramedics carried out emergency first aid before she was taken to Sunderland General Hospital, but she died later.
Her mother, Mrs Mandy Potts, 26, and brother Christopher, seven, were treated for shock and minor cuts but were later able to return to their home in the city.
Police said the Fiesta was being towed along Hylton Road when the rope snapped, with the car mounting the pavement and smashing into the shelter.
The fire station officer, Dave Ford, said: "When we arrived there were quite a few people lying around injured and we realised the young girl was seriously hurt, so we immediately directed our first aid towards her.
"We got resuscitation equipment to her then moved the car back to give us more room. Firemen and ambulancemen worked on her for a while then when we thought it was right, she was taken to hospital."
Natalie's father, Gary Hodgson, 31, who is unemployed, said: "Natalie was a joy to have around. She was any man's perfect daughter. I can't believe she's gone.
"I was doing some work for a friend in another part of town when my brother- in-law came and said Natalie had been hurt and was in hospital. I just dropped everything and went with him to the hospital.
"I tried to go down the coridoor to see her because I didn't know then exactly what had happened but a nurse guided me into a side room and they told me what had happened.
"I still can't believe she isn't with us anymore. I'm just numb.
"Mandy was taking the kids out around the town for a few hours. It was the first day of the school holidays and they were excited about being off for Easter.
"Mandy told me that Natalie was at her side running around in a little circle. She must have been excited about going to the shops.
"Then this car came along being towed by another. It swerved and then veered straight at them.
"She didn't have a chance. Mandy was just behind the bus stop and made a grab for Natalie but it was too late.
"Thankfully Mandy and Christopher weren't too badly hurt. Mandy is in a state of total shock and Christopher has some nasty cuts around his mouth and had a chunk of glass removed from his hand.
"They are back home with me but they are inconsolable. It hasn't sunk in with Christopher.
"I asked if he wanted to go down to see her after they had cleaned her up . . . but he said he didn't want to see her."
The police appealed for witnesses to the incident.Reuse content