The condition was discovered nine weeks into the pregnancy, in a scan that showed Vanellope's heart and part of her stomach were growing outside her body.
"She's been lucky, if you like, in that she has a structurally normal heart, which most of these babies don't have and she didn't have any other abnormalities with the chromosomes".
Her partner Dean Wilkins said: 'We were told our best bet was to terminate and my whole world just fell to bits'.
Fifty minutes later, Vanellope was deemed stable enough to undergo a series of surgeries with 50 anaesthetists, heart surgeons, and paediatricians, who put her heart most of the way back inside her chest.
Baby Vanellope, with her parents, Naomi (L) and Dean (R).
Vanellope had been due on Christmas Eve but she was delivered on November 22 to give her more chance of survival.
"Vanellope in the film is so stubborn and she turns into a princess at the end, so it was so fitting".
The second surgery was conducted after a gap of seven days which was to create more space inside her chest in order to make the heart fit in a more accurate manner.
The operations included making space in her chest for the heart, as she did not have one.
These babies generally have less than 10 percent chance of survival, depending upon the risks of other conditions along with the ability to place the baby's heart safely back inside the hest.
A baby may be the first in the United Kingdom to survive being born with her heart outside of her body.
Her mother, mother-of-two Naomi Findlay, said that when she first found out about the condition she "burst into tears".More news: Wreaths Across America honors veterans Saturday
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Mr Wilkins said: 'When she cried, we cried. "I felt hopeless and just held onto Naomi and was staring into her eyes praying that it was all going to be ok".
She was wrapped in plastic just after birth to protect her heart until the surgery could begin.
Consultant Neonatologist Jonathan Cusack said: 'The bag keeps the organs sterile but also keeps the tissues moist.
After around three hours of operations, Vanellope was taken to the hospital's intensive care unit, where she will stay for several weeks, "while she hopefully gets strong enough, and big enough, for her heart to be placed fully within her chest and covered in her own skin", anaesthetist Dr Nick Moore said. I had brought an outfit to hospital that she could wear if she died.
East Midlands Congenital Heart Centre lead surgeon Branko Mimic was, however, pragmatic about the birth, saying that her case is very rare because everything else appears normal.
Health Line website states that the condition affects about one in 126,000 births and treatment options are limited.
She is believed to be the first baby in Britain with this condition to survive.
'I genuinely didn't think my baby would survive, but the staff at Glenfield have been unbelievable.
Mr Wilkins, a builder, said: 'The moment she was born, I realised that we had made the right decision.
Findlay said the couple named their child after a character in the Disney film, "Wreck It Ralph".
Naomi added: "I had prepared myself for the worst; that was my way of dealing with it".
Explaining what it felt like after the birth, the 31-year-old said: 'I started to panic, I actually felt physically sick because I actually thought there was a big possibility I wouldn't be able to see her or hear her, or anything really.