It's her third interview with Sawyer since she first spoke about her horrendous experience in 2011.
Dugard was abducted at age 11 in 1991 by Phillip and Nancy Garrido in 1991. She was held captive in Garrido's California backyard compound and had two children fathered by him.
Dugard and her daughters were rescued in 2009. Phillip Garrido pleaded guilty to one count of kidnapping and 13 counts of sexual assault and was sentenced to 431 years in prison.
Nancy Garrido pleaded guilty to one count of kidnapping, one count of rape by force and to California's "one strike" rape law. She was sentenced to 36 years to life in prison.
More than two years after Dugard was kidnapped, when she was 13 years old, she learned she was pregnant and gave birth at 14 years old to her first daughter.
"I can't fathom how I kept it together or, you know, I must've been checked out, you know, on a different level. You know, [I was] present, but not present for, you know, some of it, because it's terrifying on its own. But being alone, how did I even do that?" Dugard recalled.
In 1997, Dugard gave birth to her second daughter.
"Anything could happen," Dugard said of the dangers of giving birth in such difficult conditions. "And I had two."
As she and her daughters grew older, Dugard said she planted a flower in front of the shed and set up a little school to teach them as much as she could with only her fifth-grade education.
"They're so resilient, and they're beautiful and loving, and I'm really lucky," she said.
Dugard has protected her daughters' privacy and said some of their friends don't even know of their past. She said the three of them are able to talk about what happened with each other.
"When I refer to him … I think I've been calling him Phillip lately, actually," Dugard said.
Five years ago, Dugard said she called Phillip Garrido their dad.
"They saw his craziness and ups and downs and knew how unpredictable he was," she said.
She said she and her daughters have learned to laugh at the challenging life they live together.
"To know it was OK to laugh about, you know, Phillip and Nancy and their … craziness … it helps," Dugard said.
Both Dugard and her mother, Terry Probyn, said they would not want the two girls to see their father in person, but that they would respect their decision if they wanted to meet him.
"I would hope they wouldn't want to, but as long as he's behind bars, and they're safe, then I wouldn't hinder their ability to make that choice," Dugard said.
Probyn said: "It's their decision. I would hope that they would choose not to."
Dugard said she has done everything she can to not let her own fears limit her daughters' lives.
"Do we scare our kids into never wanting to do anything or do we prepare them for the worst in life, never knowing if, you know, if it's really going to happen?" she said.
Dugard first detailed her horrific experience in her 2011 bestselling book, "A Stolen Life: A Memoir," and now has a second book, "Freedom: My Book of Firsts," about moving on after those years in captivity.
Her memoir is due out July 12.