At the time the couple were living on Anglesey where William was working as an RAF Search and Rescue helicopter pilot.
Speaking in Cardiff on Wednesday, Kate, 38, said: "It's nice to be back in Wales! I was chatting to some of the mums earlier. It was the first year and I'd just had George – William was still working with Search and Rescue and we came up here and I had a tiny tiny baby in the middle of Anglesey it was so isolated, so cut off.
"You can come here and tell people, 'I haven't slept'," said Rhi.
"And everyone else is like, 'I haven't either!'" laughed Kate. "It normalises it. No one is going to judge you for it. And it's a social thing for you.
"So many families now are so spread out," the Duchess continued. "It's much harder to rely on other generations for support."
Kate's visit came as part of a 24-hour tour to launch a landmark survey on early childhood, which she hopes will bring about "lasting change for generations to come."
The Duchess is raising awareness of the Five Big Questions on the Under Fives, a study by IPSOS Mori on behalf of the Royal Foundation, which is thought to be the largest of its kind in the UK.
Asking several parents if they'd seen the survey she said: "What do you think? There is so much pressure on parents, but actually they need the community too."
Stopping to meet the resident guinea pigs Willow and Bella in a wooden hut, she told the children: "I had guinea pigs when I was little."
She was then presented with flowers and a drawing of herself by four-year-old Erin Jones, who briefly hesitated when prompted to hand them over.
"Are you shy?" asked Naomi Asante Chambers, a senior teaching assistant.
"Don't worry, I am too," the Duchess told the little girl.
Speaking afterwards, Head of the Centre Carolyn Asante said: "It's lovely to have someone who understands children and child development."
Describing how the Duchess had helped clean a child's hand which was covered in sand, she added: "I said 'you've got the job,' and she said 'I wish!' Our children quickly gauge people who are genuinely interested in them and if they're not they just won't bother with them."
During a later visit to Send Prison, near Woking in Surrey, Kate talked to prisoners who trace their history of offending and addiction back to troubled childhoods involving domestic violence, absent parents, drug and alcohol abuse.
"It really shocked me when I came here last time how early the challenges were that you faced," the Duchess told a group of ex-offenders, including three women she met in 2015 when they were serving sentences.
One prisoner, Francesca, told Kate that the prison's 12-step drug treatment programme had changed her life, adding: "Coming to jail is one of the best things that has ever happened to me."
The Duchess smiled and said: "It's so often I hear that. Why does it have to get to that point before people receive the help and support?"