After two months apart, a Honduran mother and her young son were reunited at a Seattle airport on Saturday, in an emotional scene of the kind repeated across the US as immigrant families broken apart by the Trump administration have been brought back together.

In the minutes after their reunion at Sea-Tac international airport, Yolany Padilla’s hands did not leave her son’s shoulders. Jelsin, who is six, squeezed his mother’s hands as she offered a hopeful message to parents still kept from their children.

“The moment will come,” she said, in Spanish.

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.

Padilla, 24, and her son left Honduras in the spring, to seek asylum in America. They traveled through Guatemala and Mexico before crossing into the US in May. In south Texas, authorities immediately forced them apart.

Jelsin was one of more than 2,500 immigrant children separated from their parents under a “zero tolerance” policy announced by the Trump administration in April and abandoned, under severe international pressure, in June. A federal judge in San Diego ordered that the children be returned to their parents but the government has been slow to do so.

Padilla is now the lead plaintiff in a lawsuit against the federal government, an action she hopes will help hundreds of other asylum-seeking parents separated from their children. Padilla’s attorneys claim the government has violated due process rights as well as federal law related to the treatment of asylum seekers.

Yolany and Jelsin. ‘It has been an emotional rollercoaster.’ Photograph: Levi Pulkkinen/The Guardian

“It has been an emotional rollercoaster and it’s inhumane,” said Jorge Barón, the executive director of the Northwest Immigrant Rights Project, which is representing Padilla with an attorney, Leta Sanchez. The government has yet to formally respond.

Padilla was jailed at a Seattle-area federal detention center. Her son was sent to New York state. He spent weekdays at a youth center and nights and weekends with a foster family. Mother and son spoke by phone. Calls often ended in tears.

That Padilla was Jelsin’s mother was never in question; nor was it in doubt that she would be able to care for him. But after she was released on 6 July, she was still forced to wait more than week before her son was returned, to live with her at a temporary home in a Seattle suburb.

Padilla and Jelsin are the exception. As of Friday, the federal Department of Heath and Human Services Department (DHHS) had identified 2,551 children aged between five and 17 who were placed in its custody while the family separation policy was in effect.

On Thursday, DHHS completed a review of the cases of 103 children under the age of five. Fifty-seven had been reunited with their families; the department said safety concerns meant the other 46 remained apart. Parents of 12 of the youngest children had been deported without them and were being contacted, the DHHS said.

Padilla and her son were detained on 18 May, shortly after crossing the border with a group of migrants they had joined in Guatemala. That month, US border patrol officers apprehended 4,721 families on the southern border, as well as 809 unaccompanied children. It is not clear how many of those families were broken up.

Jelsin saw his mom briefly the following day, because immigration officials needed a photo of them together. Then their separation began.

Padilla said she spent three days in a “hielera” – Spanish for “ice box”, a phrase used by Central American migrants for the notoriously cold Customs and Border Protection holding cells – before being moved to a larger facility at Laredo, Texas.

She has described a diet of ham, frozen bread and water drawn from the tank of a toilet shared with other detainees. Ultimately, she was transferred to a federal facility near Seattle.

Padilla and Jelsin continue to seek asylum in US immigration court, an opaque administrative body separate from the federal judiciary. While most unauthorized immigrants cannot petition for legal status from inside the US, those fleeing persecution can petition for asylum. Immigrants who receive asylum status can then seek permanent residency and, if they desire, citizenship.

Báron said the government has agreed Padilla had a credible fear for her safety when she fled Honduras. That determination is a first step in what can be an extended process.