Yolany Padilla has a simple demand.

A 24-year-old mother, she spirited her young son out of Honduras only to lose him at the US-Mexico border to American immigration officials. Now she, as the lead plaintiff in a lawsuit against the federal government, hopes to stand in for hundreds of other asylum-seeking parents separated from their children at the border.

“It is time to return our kids,” Padilla said through an interpreter.

Q&A Will separated families be reunited? Show More than 2,300 children were separated from their parents under the Trump administration's "zero-tolerance" immigration policy. Although the policy has been halted after international opposition, there are concerns that promised reunions won't happen any time soon, if at all. The Department of Homeland Security says the "government knows the location of all children in its custody and is working to reunite them with their families". But attorneys with the Texas Civil Rights Project, which represents hundreds of separated families, said it has “grave concerns about the government’s ability to track parents and children who have been caught up in this crisis”. Connecting families presents an enormous challenge because once they are detained at the border, children and parents enter two separate systems: for parents, the US Department of Homeland Security and criminal prosecution; meanwhile, children are given “unaccompanied alien child” status and transferred to the US Department of Health and Human Services. With no clear process in place, it’s possible some families will never be reunited. By Lauren Gambino and Olivia Solon.

Released from federal detention on Friday, Padilla and her attorneys are pushing US immigration officials to move forward in reuniting her family and those of other parents caught up in the Trump administration’s “zero-tolerance” policy, which saw thousands of immigrant children taken from their parents at the border. Speaking in Seattle, Padilla said she hadn’t seen her son, Jelsin, since the day after her arrest in May.

Yolany Padilla and her son Jelsin, six. Photograph: Courtesy of the Northwest Immigrant Rights Project

Jelsin spends weekdays at a youth center and nights and weekends with a foster family Padilla knows nothing of. He doesn’t understand why he can’t be with his mother. Their phone calls, more frequent now that Padilla has been released, tend to end in tears.

“What they are doing is terrible,” Padilla said through an interpreter. “I just hope the other mothers who are detained will be liberated soon.”

For Padilla, holdup is largely bureaucratic and, as her attorneys describe it, needlessly cruel.

Parents like Padilla are being forced through a system of background checks and identity verifications designed to protect children who arrive in the United States without parents, her attorney Leta Sanchez said following a press conference. Immigration officials have a photo taken of Padilla and Jelsin hours after they were detained.

Sanchez said she had been told it may take up to 60 days for the checks to be completed.

“Every day that Jelsin is withheld from his mother, the damage that has already been caused is perpetuated,” Sanchez said during a press conference at the Seattle office of the Northwest Immigrant Rights Project, an advocacy organization representing Padilla.

“This is a six-year-old boy,” she continued. “He needs his mother.”

Padilla and two other Central American women separated from their children sued the federal government in late June demanding that they be reunited. A similar legal action prompted a federal judge in San Diego to order federal authorities to reconnect arrested immigrant parents with their children.

The women’s children were among the 2,000 to 3,000 separated from their parents at the border this spring. The separations, which saw parents detained and children placed in distant foster homes and youth centers, has reinvigorated a national discussion of immigrant rights and immigration policy.

Losses in court forced the administration back from its zero-tolerance policy. The government has been given until the end of July to reunite the families, though it has already missed a Tuesday deadline to return the youngest children to their parents.

Jorge Barón, the executive director of the Northwest Immigrant Rights Project, said it had only just begun to investigate their asylum claims and had found Padilla had a credible fear for her safety when she fled Honduras.

Yolany Padilla speaking in Seattle. Photograph: Elaine Thompson/AP

She and her son were arrested on 18 May shortly after crossing near Hidalgo, Texas, with a group of migrants she joined in Guatemala. As Padilla described it, immigration officers joked about bombing Central America to kill would-be immigrants.

Padilla said she was separated from Jelsin on the day of the arrest. They were briefly reunited for a photo the next day, and she hadn’t seen him since.

Padilla said she was held in what she called an “ice box” for three days before being moved to Laredo, Texas. She described subsisting on ham, frozen bread and water drawn from the tank of a toilet she shared with other detainees. Guards, she said, wore masks when interacting with detainees because of the smell.

Conditions improved when she arrived at a federal detention center outside Seattle, but weeks passed before she was able to learn that her son had been moved to upstate New York.

Padilla’s attorneys claim the government has violated their due process rights as well as federal law related to the treatment of asylum seekers. Requests for comment made to the Department of Homeland Security were not immediately returned.

Asked whether she believed the separations would deter other Central American families from heading north, Padilla said no.

“People are seeing what’s going on,” she said, “and they have not stopped.”