Jaycee Dugard Speaks, Shares Family Moments in Home Video

updated 03/05/2010 AT 11:50 AM EST

originally published 03/05/2010 AT 08:50 AM EST

Life looks back to normal for Jaycee Dugard as she speaks on TV for the first time since being released from 18 years in captivity.

"Hi. I'm Jaycee," the 29-year-old Dugard says to the camera. "I want to thank you for your support and I'm doing well ... It's been a long haul, but I'm getting there."

To illustrate her point, she bakes cookies with her mother and half-sister, Shayna, 19, and she laughs a lot on the exclusive home videos ABC aired Friday morning on Good Morning America.

"We released this video so that you can see that we're happy and well and when we have more to share we will," Terry Probyn, Jaycee's 50-year-old mother, says of the clips. Though she added: "As a mother I am pleading for our privacy in this very public story."

On the home videos, most of the talking is done by Probyn, who thanks supporters for "all the love and support" they've shown these past few months and says, more than once, that they want to be left alone "during our healing process."

"It is our desire to share the miracle with the world," Probyn says. "But it must be done on our terms." Dugard lives in seclusion with Probyn and the two daughters – Angel, 15, and Starlit, 11 – fathered by her alleged kidnapper, Phillip Garrido.

Probyn also clears the air about a northern California church that was collecting money for the family. "We did accept financial support from an undisclosed benefactor and have no affiliation with any church. Please give us the time to heal as a family, without the prying eyes of the photographers and the press."

ABC is also set to air Dugard's video on 20/20 and Nightline.

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