While their mothers – who are sisters – were likely to both have the chromosome, it was extraordinarily rare that the girls' fathers both had the defect.
Charlotte, eight, has a severe form of SDS, which means she can spend weeks in hospital, while Kimberley's condition is controlled at home with 15 different vitamins and tablets.
The effects of SDS vary in different people, but it mainly causes problems with digestion, the pancreas, bone marrow and skeleton, but other organs may also be affected. It lowers immune systems and puts sufferers at a high risk of fatal conditions, most commonly leukaemia.
The girls cannot absorb the nutrients they need from their food naturally and so they have to endure regular hospital visit for blood tests and bone marrow checks.
Both girls suffer from respiratory problems and Charlotte uses a wheelchair.
Charlotte was diagnosed with the condition after she failed to thrive and ended up in intensive care and had to be resuscitated three times.
Eventually, when she was 18 months old, her parents Joanne and Glyn were told she was suffering from SDS.
Meanwhile, Joanne's sister Jules was pregnant with Kimberley. Six months after Kimberley was born she too began to show some of the tell-tale signs of SDS, refusing feeds and vomiting.
"I already had a daughter, Georgina, so instinct told me there was something different about Kimberley." She was referred to a paediatrician when she was seven months old. It was then that SDS was suggested to Jules and husband Paul, 45.
"The doctors said that she could have SDS, we just wouldn't believe it," says Jules, 41.
"Although Joanne and Glyn had both been confirmed as carriers, Paul and I were convinced it was impossible we would be too. We agreed to the blood tests to rule out SDS."
To the family's horror, Kimberley had the same condition as her cousin. "We were completely stunned," Jules explains. "My first question was: 'Is Kimberley going to die?' and the doctors said they couldn't see beyond nine years of age. We were horrified."
Coming to terms with SDS has been traumatic for both families, especially as the girls are now more vulnerable to leukaemia. Both have regular blood tests.
"We go St James's every three months for blood tests and to have a bone marrow checked. If her bone marrow were to fail, she would have to go on the national register as none of the family is a match," says Jules.
"We go to hospital so often I think Kimberley is just used to it now. Sufferers of SDS are much more susceptible to picking up infections and illnesses. If Kimberley ever got cancer, then it would be the death knock for us. That's why the doctors are constantly monitoring her."
The illness has restricted their growth. Charlotte has had to have her teeth removed because the acidity in her saliva has caused them to rot – another symptom of SDS.
Fortunately, Kimberley's strain of the condition is controlled with a concoction of vitamins and a drug to help her digest food. Jules said: "We know it's highly unlikely a cure will be found during Charlotte and Kimberley's lifetimes so we need to give the girls the best possible lives."
Despite their disabilities, both girls go to mainstream school, although Jules said SDS also causes some behavioural problems and learning disabilities.
"There are only 300 people in the world with this condition and each one seems to be a bit different. There are different spectrums to it and so the doctors find it difficult to know what will happen."
The oldest person Jules has found with SDS survived in to their 40s, but the family are concerned that they do as much as possible with Kimberley while they can.
"We just don't know what is going to happen. There is some research going on into SDS but not that much, and nothing that will help our children," says Jules.
So she and Joanne set up the KC Dream Foundation to raise money for children with SDS in a bid to bring some happiness and enjoyment to their lives.
"At the moment there is no national register of people with SDS in Britain although they are planning to start one.
"We know of a boy in Hull and another in Lincoln with it and we raise money by doing silly things to give them a holiday or an iPod, anything that will bring them enjoyment while they can.
"It also helps me to have something to focus on. It is hard on the whole family when you have a poorly child."
At the weekend Jules will be dressing up as a Dalmatian to cycle the 101 miles from Leeds to Hull to Lincoln, linking three child sufferers of SDS.
"I want to raise money for the children but also to raise awareness of the condition," says Jules.
They are also organising a fund-raising Midsummer Sparkle Ball – Friday, June 18 at the Cedar Court Hotel, Wakefield.
For more information, visit www.kcdream.btik.com or email [email protected]