In North Carolina, for example, second-parent adoptions for same-sex couples were outlawed in 2010. Only stepparents who are legal spouses or the biological parent can adopt. Gay marriage is not legal in that state.
Even those couples who lived in "friendly counties" around the state's urban centers who previously had such rights, had them revoked when a judge invalidated their adoptions.
Now, with the help of the American Civil Liberties Union, six same-sex couples have filed a lawsuit to fight the ban , saying it violates their constitutional rights and is discriminatory. They hope to take it to the Supreme Court.
When LGBT families are banned from being foster parents or adopting, children are denied permanent homes and remain in state care instead, according to studies from the Evan B. Donaldson Adoption Institute.
"The best interests of children should always be paramount," said its executive director, Adam Pertman, in a prepared statement. "With more than 400,000 children in foster care and more than 100,000 children awaiting adoption, it simply makes no sense -- and certainly isn't to their benefit -- to deny children a forever home with qualified and loving parents simply because those parents are gay or unmarried."
In widely different policy, California allows same-sex couples to pursue second-parent adoption. Going one step further, the state Senate is expected to pass a law allowing multiple parents to act on a child's behalf, as an effort to keep children out of foster care in case of death or divorce.
The bill sprang from a 2011 appellate court decision that placed a girl in foster care when her legally married parents -- two lesbians -- could not care for her. The child was taken into state custody when one of her mothers was jailed and the nonbiological mother was hospitalized.
The court did not have the authority to appoint the girl's biological father, with whom she had a relationship, as a legal parent.
As for Liuzza, he never dreamed his son would be taken away. "I thought we were equal like everyone else," he said.
But after he initiated a separation because of problems in the relationship, Liuzza said his partner sought genetic testing.
Just before the boy's sixth birthday, his partner used his rights as the legal parent to take the child away.
"I showed up at school one day to pick [the boy] up and he wasn't there," said Liuzza. "I called my ex and he was on a plane to Dallas. The school had no idea. My son had no idea. I had no idea."
Now, he only sees his son once every two months and his ex-partner times the phone calls to 20 minutes twice a week. Although Liuzza has generous health benefits, his ex-partner does not, and the child hasn't seen a doctor or dentist in months.
In California, where he has gay friends who both have legal rights, Luizza said, "if David and David separated, they would be able to fight it in court."
"It's the hardest thing," he said. "And the only way I can get through it is knowing that when my son is 16 or 17, he can make the decision where he wants to live."
Liuzza hired two lawyers and spent "so much money" to make himself a legal parent, but to no avail.
"I couldn't do it," he said. "I am virtually a stranger … Frankly, biology in this state is more important than experience and caregiving."