"When they go someplace like that, they forget about what they have to go through," said their mother.
"They can be kids and not worry about the responsibilities of -," she said, her voice trailing off.
Zane and Alexus suffer from type II spinal muscular atrophy, a hereditary disease that causes weakness in the arms and legs. Both use wheelchairs. The Dicks have a third daughter, 1-year-old Ava.
In April, the family organized a charity walk and raised $10,000 for research into the disease.
Squeo contacted Becky Dick a few weeks ago to tell her the children had been nominated to be recipients of his charity, Baking Memories 4 Kids. (A cousin of Squeo had met the family at a fund-raiser and recommended the children.) Once Dick realized Squeo wasn't a telemarketer, she was floored, she said.
"The fact that these kids live with a debilitating disease every single day of their life - they miss out on so much," she said.
Squeo says helping children like Zane and Alexus is something of a calling. In 2006, he was hiking in Arizona when he felt a lump in his neck. When doctors removed the lump, they realized he had advanced testicular cancer.
"It was literally days away from entering my brain," Squeo recalled.
Surgery and three months of chemotherapy followed. In March, he started the foundation for children with life-threatening illnesses.
"I'm a big believer that everything in life happens for a reason," he said.
People nominate children through the foundation's website, bakingmemories4kids.com. For the charity's inaugural holiday season, Squeo and about 40 volunteers are using a family recipe to bake the cookies and raise money.
The 180 containers of cookies, sold for $24.99 each, were enough to send the Dick family to Orlando for a week of their choosing. For each order, Squeo sends $1 to St. Jude's Children Research Hospital in Tennessee.
Squeo has 10,000 more cookie containers in his garage. His foundation has raised enough money to send eight to 10 families to Disney World next year.
Knowing that Squeo had been through a similar ordeal made Becky Dick appreciate his gesture even more. "He is like the uncle you never had," she said. "Just so loving and so caring."