Hayley Okines was 21 months old when doctors at Great Ormond Street hospital in London told her mother that she was unlikely to live past 13. Kerry Okines remembers vividly how she felt hearing those words in 1999 – numb. She was anaesthetised by disbelief and premature grief. Shock turned into depression that rapidly spiralled to suicidal –and even infanticidal – thoughts.

"We knew it would happen, we just didn't know when," recounts Kerry, 37, in the candid memoir of her family's struggle with the condition progeria, Old Before My Time.

But 12 years, and hundreds of hospital visits, have passed since Hayley was diagnosed with Hutchinson-Gilford progeria syndrome, and the understandable fatalism that first shrouded the family has gradually evolved into a more positive, tempered realism.

"There's a lot to be positive about. A lot of things have changed since Hayley's diagnosis. They've identified the gene, different treatments are developing – there was none of that 12 years ago, so you always hold on to that bit of hope," says Kerry from the family's home in Bexhill-on-Sea, on the East Sussex coast. "When Hayley was first diagnosed, I couldn't imagine her being here tomorrow let alone going to primary school or even secondary school. It was incredibly difficult to deal with in the beginning."

In the book, Hayley is remarkably frank about her future: "I'm not worried about dying. They said the Titanic wouldn't sink but it did, so that proves experts can be wrong and I want to prove the doctors wrong. Deep inside, I am no different from anyone."

It's a view echoed by her mother. "Apart from her progeria, Hayley is just like any other stroppy teenager."

It's an admirably sanguine depiction of domestic normality, but the truth is rather more complex. Hayley's progeria, which affects one in 8 million children, means that she ages eight times faster than the average person. She is one of only four children in Britain and one of only 74 in the world with the condition, whose symptoms mirror the conventional degenerative signs of old age.

In common with most other children with progeria, Hayley's growth is severely limited – her nine-year-old brother, Louis, and sister, Ruby, six, tower over her frail physique and she is currently wearing clothes designed for six-year-olds. She is also susceptible to heart and cardiovascular problems, kidney failure, stiff joints and hip dislocations.

The difficulties faced by the family sadly proved too great a strain on Kerry's marriage to Hayley's father, Mark, which ended in late 2010. "It's a bit more of a struggle now that me and Mark have separated," says Kerry. "Obviously it's harder being a single mum, but we share the care and although progeria was a major factor I can't blame the split completely on it.

"People cope with things differently. It either brings you closer together or it pulls you apart. Right from the beginning, Mark was very much looking into the medical side of things and seeing if we could find other families, whereas I would be quite happy just sitting at home and looking after Hayley in my own way. You could see from the beginning that we were going to go in different directions."

Kerry and Mark were united on one thing from the start: the desire to minimise any potential psychological damage to Hayley caused by strangers' cruel stares and comments.

So rather than retreat into a non-threatening reclusive lifestyle they embarked on a very public mission to further the world's limited knowledge of progeria by appearing in a series of documentaries for Channel Five's Extraordinary People series. The result is that people do stare at Hayley but mostly to say, "Oh look, it's that Hayley off the telly."

Being on television has also opened doors normally closed to celebrity-obsessed teenagers. Hayley's burgeoning list of high-profile encounters reads like an A-list Who's Who? "I met Simon Cowell once. Kylie Minogue. And I met Justin Bieber for my 13th birthday," she says, in a voice as slight as her tiny frame. "And Cheryl Cole and Nicola Roberts from Girls Aloud. And Max from the Wanted said he loved me."

The cloud over this silver lining for Kerry is balancing the delicate dynamic between Hayley and her younger siblings. "Inevitably, Hayley does get more than the others and a lot of people used to say to me, 'How do you say no to Hayley?' But you have to. You have to find that fine line between being spoilt and making her feel special, but the truth is that nine times out of 10 I give in to Hayley."

Progeria has meant all the Okines children are more mature emotionally than most of their peers. "Hayley has definitely had to grow up a lot quicker. Normal teenage girls don't have to worry about whether tablets are going to make you ill or make you better, or when you've got to have your next lot of bloods done. She's had to become old beyond her years. It's also had an effect on her sister. Ruby is a very mature six-and-half-year-old."

This statement provokes shrieks of hysterics from Hayley, who clearly doesn't agree: "Ruby is a terrible tantrum thrower," she says. "I try to be the boss but they ignore me, so I do sometimes throw things at them."

"You see what I mean? We're just like a normal family."

Normality in January 2012 for Hayley will mean a week in intensive care, followed by 10 weeks recovery after an essential operation to repair her dislocated hips, which mean she can't walk unaided at the moment.

"There's no guarantee that it will be successful and she'll be able to walk, but we haven't really got a choice," says Kerry. "It's either be immobile for the rest of her life or go for an operation and see if it'll work."

The family are also waiting for results from a pioneering US drug trial in which Hayley taken part for four years: "In the beginning we were thinking, maybe we're only a week away from a breakthrough – but we're still waiting."

Kerry admits that Hayley's limited life expectancy is never far from her thoughts. "We had bereavement counselling when Hayley was diagnosed. I can't remember much about it and it didn't feel like it did much good at the time, but I think it obviously does now. I do think about it but don't talk about it. We don't sit there and say, 'Is this what you want?' or, 'What songs do you want?'

"But I do write little things down, things that might be quite nice. Then I put it in its box and put it away."

Hayley, on the other hand, is bursting with plans and excited by the future: "I want to open a beauty salon with my friend Erin – or maybe I'll be a stylist for the Wanted. And I want to bring out my own perfume too, like Justin Beiber. And when I pass my driving test I want to get a red Mini Cooper.

"But my biggest wish for 2012 is just to be able to walk by myself again."

Old Before My Time: My Life With Progeria, by Hayley and Kerry Okines is published in paperback by Accent Press, £9.99. To order a copy for £7.99 with free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846