Prince William's wife, who is a champion of the hospice movement at home in the U.K., where she is patron of East Anglia Children's Hospices, was keen to see one on her travels to New Zealand.
Visiting the Rainbow Place home in Hamilton, the 32-year-old duchess met children with life-threatening illnesses as well as those suffering from grief and loss, or coping with parents who are terminally ill.
She also toured a Mad Hatter's tea party for children and their families held in a teepee-style tent in the garden.
Nurse Gail Sargent, who accompanied Kate as she met the youngsters, tells PEOPLE: "It was like magic, like a spell had been put on me. She was natural and normal and child-focused. I found it like an aura."
When she spoke with the home's terminally ill children, Kate was both compassionate and forthright, caregivers say.
"She wasn't afraid to ask about how tough it was to have to do the treatments," Sargent explains. "She's clearly interested in children and talked about baby George to one child who asked about eating vegetables. And she said George has to eat his vegetables, too."
Adds Lynne Henderson, another nurse, "She was so smiley and put the children at ease."
During her visit, Kate had a private meeting with Sam Ogilvy, 12, whose father drowned two years ago. To help him explain his story to the duchess, Sam used a sand tray – a play-therapy tool meant to help youngsters express themselves more fluently.
Sam says: "I told her about my journey by using the sand tray. She was really nice. She quite liked the sand-tray idea of telling the story."
'She Touched So Many People'Then, in a play-therapy room, Bailey Rupe, 6, showed the duchess how she uses hand puppets to explain how she's feeling about her mother's terminal breast cancer.
"Are you having tea? Can I sit with you? How is mummy doing?" Kate asked Bailey. "Do you find it difficult sometimes? Yes, I'm sure you do, but you're a very brave little girl."
Bailey said afterward, "I was excited to meet a real princess, and it made me feel like a princess for the day, too."
The hospice's chief executive, Craig Tamblyn, tells PEOPLE that Kate – who also witnessed an art-therapy session – "showed interest in every child – she's a really kind-hearted person."
Tim Buys, whose brother has cancer and is staying at the hospice, underscores the significance of Kate's visit. "Seeing the looks in the young children's faces, you could tell they were blown away," he says. "She touched so many people here."
After leaving the main building, the duchess went to an Alice in Wonderland-themed Mad Hatter's tea party filled with cakes, a cotton-candy machine, carnival games and a Narnia wardrobe that opened onto a snowy back room.
Hamish Taylor, a 17-year-old whose muscular dystrophy has left him using a wheelchair, gave Kate a gift: a gray onesie for Prince George embroidered with the young royal's name.
"She said 'Thank you very much, I can't wait to show it to him,' " Taylor recalls.
As Kate was leaving, she was handed a bouquet of cream flowers from Kaiya Miller, 6, who has cystic fibrosis.
"I thought the duchess would have smiley eyes," says Kaiya. "And she did!"