Kimbler had taken the children to the park in his taxi cab. The vehicle was found parked near the visitor's center Monday.
The family had no food or water when they were rescued, but Kimbler said they drank water they found in the park. Meanwhile, mild weather — with low temperatures in the 60s — helped the family endure three nights in the wild.
"I don't know if it's luck," Gurtler said, of finding the family just hours before storms move into the area Tuesday. "It just worked out, fortunately, in our favor."
The park has marked trails, but beyond the paths are tangles of old growth trees, swamps and underbrush. The land has become even more rugged since an ice storm in February knocked down thousands of trees and limbs.
Tammy Ballard, the children's mother, was at the park during the search, walking down trails, calling their names.
"It's been tough," Ballard told the AP in the hours before the children were found. "I see so many footprints out there."
The park was to reopen to visitors later in the day.
Kimbler had been out of his children's lives for a few years but recently started to get them on the weekends, said Chris Ballard, stepbrother of the children. The trip to Congaree National Park was the first time he had been out there.
Jeffrey Collins in Columbia contributed to this report. Kinnard can be reached at http://twitter.com/MegKinnardAP