"We were alone in the middle of the ocean and in deep trouble. My hands started shaking. It was the loneliest feeling in the world."
Suddenly, a massive wave crashed over the back of their boat, sending water careering through the catamaran's saloon and washing Bobby and Cheryl inside, where they were greeted by the sight of their two terrified children who had been sleeping minutes before.
"That's when survival mode kicked in," says Cheryl. "I told the kids to grab their lifejackets and warm clothes and prepare to abandon ship."
The extraordinary story of the Coopers' miraculous rescue made global headlines last week when they were plucked off Beveridge Reef in the middle of the South Pacific, 130 miles from the nearest landfall, the tiny island of Niue, a speck in the ocean 1,500 miles north-east of New Zealand.
By chance, a whaling research ship, the Dona Catharina, was seeking shelter from the storm in a bay just a mile from the Avanti when the Coopers sent out a panicked Mayday signal.
"It's incredible to think the Dona Catharina was there, in the middle of nowhere," says Cheryl. "They saved our lives and I can never thank them enough."
Speaking about their ordeal for the first time last night after arriving on Niue, the relieved family told The Mail on Sunday about the moments of dark humour that lightened their ordeal - and hit back at critics who have branded Bobby and Cheryl "irresponsible" parents for placing their children in grave danger.
Despite having endured a night of terror on a boat stuck on a reef amid heaving seas, Cheryl was still able to tell of the hunky rescuer called Manu who emerged "glistening from the sea" at first light as the battering tide relented, his long, dark hair flowing behind him "like a male Ursula Andress in a Bond film", to carry them to safety.
And Bobby responded angrily to being branded foolhardy parents, saying: "Kids today are mollycoddled. Our children have learned more about the real world on our adventure, including this accident, than they could ever learn from a schoolbook." Bobby, an experienced sailor who has logged more than 200,000 miles at sea, says the accident happened because his high-tech GPS navigational system failed to show the reef.
"We were using electronic navigation charts on a 100-mile scale which should have shown where all the islands are, where all the reefs are. But it showed nothing.
"Once we hit, I started scaling the chart down and when I got to the 12-mile scale, the reef suddenly appeared. It was a huge shock. I had no idea it was there. We've lost everything. All we have left is four bin bags of stuff. But possessions mean nothing. Our family is irreplaceable. We've got nicks and bruises but no serious injuries."
Bobby, raised in Stirling, Scotland, is a lifelong sailor who cheated death once before in 1984, aged 19, when the tallship he was sailing on, the Marques, sank with the loss of 19 lives, including four Britons, in the Bermuda Triangle.
He returned to the UK but realised "land life' wasn't for him - and set off back to sea. By the early 2000s, he was working as a boat repairman in Palma, Majorca, when he met Cheryl, from Doncaster, in a bar. Cheryl had little experience of sailing, but she was quickly infused by his passion and the couple raised their two children to love the ocean.
The pair married in 2007 and made the fateful decision to set off on their epic journey before their children grew too old to want to spend time as a family.
"When kids get to a certain age, 14 or 15, they stop wanting to do things with their parents," he explains. "Cheryl and I realised last year "it's now or never"."
The pair sold their home in Majorca and bought the £275,000 Avanti, a Privilege 465 catamaran which they picked up in the British Virgin Islands in May 2016.
It had been an "epic" adventure as the family sailed around the Caribbean then down to Panama, through the Panama Canal and explored the Galapagos Islands, before sailing on through French Polynesia and the Cook Islands. They planned to sail on to Niue, Tonga, Fiji and then New Zealand by year's end.
Cheryl says their children, tanned, fit and "incredibly self-sufficient", are "not like shore kids".
"They are non-materialistic. When our kids have birthdays they make gifts out of shells.
Robbie knows how to shimmy up a palm tree and hack a coconut open with his machete.
They've learned geography, geology, biology, calculus, all from being in the real world, from sailing and interacting with fascinating people we've met.
"Of course, we all have computer tablets. It's a great way to keep in touch with family and friends. But we don't have wi-fi very often, which forces the children to entertain themselves. Lauren loves botany. Robbie loves to fish."
The children are remarkably sanguine and upbeat, considering they stared death in the face a week ago.
Safe on dry land, mop-haired Robbie bounces around the room as he says: "I love our life.
Now every day is different. Dad taught me to catch a fish, gut and cook it. It's brilliant. If you don't like somewhere, you move on."
There was no moving on a week ago. Moments after the Avanti smashed into the reef, knocking out the propellers, the children went into "auto pilot mode" to help their parents prepare for the worst.
"I wasn't scared," insists Lauren. "We've been drilled for emergencies. A big wave hit and I was knocked off my feet. It felt like a car crash. We were getting tossed about on the reef.
Mum was on the radio calling for help and dad was on the satellite phone.
"Robbie and I grabbed pillowcases and stuffed them full of bottled water, canned food, medications; stuff we would need if we had to get in the life raft.
"I took my favourite botany books and my computer tablet. Robbie grabbed his Nintendo and penknife. He also grabbed the schoolbooks, much to my dismay."
Bobby was preparing to relieve his wife on night watch when the impact happened around 3.50am.
"The boat came to a sudden stop. There was this awful grinding, crunching noise," he says. "We swung around violently. I ran on to the deck."
Cheryl, battered by 45mph winds, was struggling to understand what had happened. "There were huge waves coming over the boat but these were white water breakers, like you get in shallow waters," she says. "I screamed at Bobby, "The sea looks crazy! What's happening?" "
After a massive wave hit the stern, snapping the keel and flushing the couple inside the main saloon, Bobby frantically called for help on the satellite phone but to no avail. So they set off their emergency beacon, while Cheryl started calling "Mayday, Mayday" over the VHF radio. The situation appeared grim, to say the least.
Bobby says: "The floorboards were lifting. Every eight to 12 seconds, we were kicked up by a wave and hurled further on to the reef. The boat was breaking from the bottom up.
"The noise was terrible. The sails were flapping and there was the grinding noise of ten tons of fibreglass being violently dragged across the reef. You could see holes appearing in the bottom." But catamarans like the Avanti are known for stability. Bobby adds: "We were ready to abandon ship. We had our important documents laid on the table but she stayed stable."
After 50 agonising minutes, they were thrown a miraculous lifeline. Cheryl says: "I heard this voice on the radio: "We can see you. We're in the lagoon."
It was the Dona Catharina, en route from New Zealand to Niue when it was also caught in the storm and had limped into a nearby cove to shelter.
At any other time the Coopers would have been days from rescue and had the catamaran dislodged from the reef it was so mortally wounded it would have sunk in deep waters.
Instead, in the middle of nowhere, the Dona Catharina turned on her lights. "It was the loveliest sight in the world," says Cheryl. "We were firmly wedged on the reef.
Overwhelming relief washed over me.
"I did what any sane British person would do and put the kettle on. We sat and had a cup of tea."
As the tide receded, the Avanti was perched precariously on the reef. At first light, the Dona Catharina launched two small dinghies but could only get within 200 yards of the catamaran.
"It was too dangerous to come any closer because of the reef," says Cheryl. Then a rescuer they would later learn was called Manu jumped into the water. "He was wearing a wetsuit and he emerged up on to the reef, walking very slowly because the reef was sharp and dangerous. He looked like a male version of Ursula Andress. He got to our boat and asked, "Is it OK if I come aboard?"
Manu carried the children, one by one, back to the dinghies which set off for the Dona Catharina. He then returned for Bobby and Cheryl.
As they turned back to look at the Avanti, its stern fully submerged in the water, Cheryl choked up. "It was devastating to see her like that, like a wounded animal."
Were they afraid of the notoriously shark-infested waters?
Bobby grins. "Sharks were everywhere, the place is swarming with them. They're not a problem. We're not part of their food chain."
On board the rescue ship, the exhausted family had time for more banter: "Being foreigners, they only had camomile and peppermint tea, not real tea," Bobby says.
Later that day, he returned to the Avanti with members of the rescue crew and salvaged a few more items, including a box of "proper" PG Tips.
And at high tide they managed to dislodge the catamaran from the reef and anchor her in the lagoon.
They took pictures and have already filed an insurance claim to cover all costs of their rescue.
Friends have set up a crowdfunding site which has raised more than $42,000 to help the family with their expenses.
The Coopers had to stay on the Dona Catharina next to their stricken catamaran until late on Wednesday, when the weather was finally good enough for the research ship to sail for Niue.
Safe at last, none of them want to give up on their grand adventure.
Lauren says: "I love life on board." She wants to return to her studies of local flora and fauna, while Robbie dreams of swimming with sea turtles again.
Bobby says: "Don't underestimate kids. They are resilient. We feel stronger than ever to have survived this as a family. We intend to carry on. Our adventure is only just beginning. Why would you stop sailing?"
If the catamaran cannot be repaired, he will almost certainly build or buy a new one.
"I have to meet with government officials in Niue on Monday and also find out what the insurance company has decided," he said.
"The boat can't be left there. Whether we salvage or scrap it, the boat needs to be brought out regardless."
If the Avanti can be repaired, the catamaran could be towed to Tonga, 375 miles away, where shipbuilders could restore the damaged vessel.
Whatever the outcome, the Coopers are determined to stay afloat.
