"It's so hard for a parent to be away from their kids," Madrid said Friday afternoon through an interpreter at a news conference. "I was so desperate and concerned."
Now Madrid says she's looking forward to a future with her daughter, Alisson. They will live with family in Houston and will have an asylum hearing at a yet-to-be determined date, said Madrid's lawyer, Thelma Garcia.
"I am happy and it's a pleasure to be with her, especially because we are together and we are with the family," Madrid said of her daughter.
A grinning Alisson also spoke at the news conference, saying she missed her mother while they were apart.
"I was happy because I was able to see her and hug her," she said through the interpreter. "I was away from her for a month and I was really happy when I saw her."
Madrid said she was not able to talk to Alisson for nine days, and for weeks she was in the dark about when they'd be together again. There were times she thought that might never happen, Garcia said.
Madrid told CNN she fled El Salvador with her daughter because she wanted to offer her daughter something more than the poverty and violence of her homeland. She said Alisson was once nearly taken from her arms during a kidnapping attempt at a market.
Alisson was heard pleading with officers to call her aunt, reciting for them the number her mother said she memorized during the 17-day journey from El Salvador to the US border.
"Mommy says I'll go with my aunt and that she'll come to pick me up as quickly as possible," Alisson said on the recording that was widely shared online.
The person who made the recording gave the audio to civil rights attorney Jennifer Harbury, who provided it to ProPublica.
"I don't want them to stop my father," a child whispered in Spanish on the recording. "I don't want them to deport him."
Cries of "Mami" and "Papa" were heard. An adult on the recording compared the wrenching cries to an "orchestra."
Madrid first heard part of the audio on the news and recognized Alisson's voice. She had made numerous calls to the shelter housing Alisson and had not been able to speak with her.
"God put an angel in her path to record that audio," Madrid told CNN last month. "That started everything."
Garcia said the reunification was a confusing process, with authorities saying it might happen Saturday in Arizona, where Alisson was being detained. Airline tickets were purchased, Garcia said, but officials then said Alisson would be brought to them in Texas.
At the airport, Madrid was told to go to one gate, then another, Garcia said. At the last minute, they were told local supporters who accompanied them could not watch the moment mother and child came together, Garcia said.
"It seemed like a political move to us," she said. "Everything was kind of hush-hush."
Garcia said the recording of Alisson's voice caused the reversal of Trump's policy.
"Her voice is what, I think, exploded the Trump policy of separating families and keeping it quiet," she said. "Nobody actually knew about this before the baby came up and said, 'Call my aunt. This is her phone number. Could you please call my aunt?' And had that audio not been sneaked out and not been brought forward the way it was, nobody would have actually known."
Garcia also said she doubts immigration authorities will be able to reunify separated children and parents in a timely fashion.
"There are a lot of children lost in the system," she said.
CNN's Darran Simon contributed to this report.