Mom: 'I'm a Terrific Divorced Dad': Noncustodial Moms Increase, Despite Social Pressure

June 14, 2013— -- They talk over Skype, swap recipes and share relationship advice via email. No, they aren't pen pals -- Talyaa and Serena Liera are mother and daughter, living 2,800 miles apart.

Talyaa Liera is a noncustodial mother – a mother without physical custody of her children. While she lives in Seattle, her three children live with their father in Pennsylvania.

Watch the full story on "20/20: With Parents Like These" TONIGHT at 10 ET.

It's an arrangement Liera said was necessary after a difficult divorce.

"There was an enormous amount of conflict, and it was wreaking havoc on my children," she told "20/20" co-anchor Elizabeth Vargas. "I felt I had no other option but to take myself out of the equation and possibly sacrifice my relationship with my children to make things better for them." Liera's ex-husband, David Woosley, disputes this account, saying there was no conflict.

Despite the distance, Liera said, their bond is strong.

"We talk all the time. We're very connected," she said. "My kids are totally wired, so we IM every day, we Skype frequently. I do the best that I can in my circumstance, and my heart tells me that I'm a good mother."

While Liera's situation is rare, she is certainly not alone. There are an estimated 2.4 million noncustodial mothers in the United States. The title carries a stigma, one author, Rhana Reiko, says branded her early on.

"I got death threats, people telling me that I am evil, that I'm human garbage," she said. "Immediately, the response was that friends of mine would cross the street to get away from me."

That harsh judgment, Reiko argues, is because society holds mothers to an impossibly high standard.

"People have this idea of what a good mother is; I don't fit that mold. But I definitely fit the mold of a terrific divorced dad," she says. "I think if I was a man, none of this would be an issue."

Reiko said she initially didn't want to have children, citing her own mother as an example of "the perfect mother" she didn't envision herself becoming.

"I didn't have a model for the motherhood that I wanted. I had this idea that motherhood was this very prescribed role that I didn't want in my life. I think that was one of the biggest stresses, that I couldn't see my future for myself," she said.

Her family arrangement has worked out for everyone, Reiko added, and has set an example to her two teenage sons for nontraditional gender roles.

"They've seen their mother make a new path. I think they appreciate strong women who can do what they want in the world and what they need in the world even if there is no model," Reiko said.

For Liera, the message that there's more than one way to mother has become the basis for a blog she created titled The Better Mothers Project.

"I think that better women make better mothers," she told Vargas. "When you love and know yourself, then you can be a better mother to your children.

But with this arrangement has come adjustment, especially for Talyaa's daughter Serena.

"When she first left, it was really difficult. I would cry all the time. It was really hard," she said. "But now, I'm not that way. I'm more me, I think, than I was before, because I figured out who I am without my mom."

Despite the challenges, Liera's children said they understood why their mother left and have been able to form a relationship with her.

"When I realized that she really is happier, I can be happy without her being here all the time," Serena said. "I really love my mom a lot."

While Serena cherishes her relationship with her mother, her vision of how she sees herself as a mother someday is strikingly different.

"As a mom, I never want to be apart from my children," she said. "I want to make that perfect family that she couldn't have. Of course, we'll have our challenges, but we'll always be there for each other in the end."

Watch the full story on "20/20: With Parents Like These" TONIGHT at 10 ET.