In a thick fog, with the Pacific Ocean lapping nearby, the family sprinted into California, joining thousands of migrants who have made their way into the country to seek asylum despite increasingly urgent government efforts to stop them.

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In Trump’s first two years in office, his administration has tried to narrow migrants’ chances to qualify for asylum, slow the number allowed in at legal checkpoints and deny protections to those who crossed the border illegally. The government tried filing criminal charges for all who crossed illegally with their children, a measure that led to the separation of thousands of family members last spring.

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But many of Trump’s plans have been blocked or temporarily halted in federal courts, and the number of families coming in continues to rise.

Some, including Estrada’s, seek the relative safety and minimal cost of a locally organized caravan, like the latest group that departed from Honduras this week . Others are smuggled through remote, rugged passes, including two young children who died in U.S. government custody last month.

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Estrada’s story illustrates why U.S. efforts to keep the families from entering the country are not succeeding — a combination of unrelenting demand, limited detention space, restrictions on how long children can be detained and how fast they can be deported.

It also makes clear the significant obstacles that migrant parents and children face once they arrive.

Trump took to Twitter on Dec. 20 to berate the caravan in which Estrada traveled and claim that the military, and immigration and border agents, had successfully kept its participants out.

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“Remember the Caravans?” he wrote. “Well, they didn’t get through and none are forming or on their way. Border is tight.”

At that moment, Estrada, 34, was 250 miles past the border, in central California, staying in the modest two-bedroom bungalow of a half sister and brother-in-law she barely knew.

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She had a monitoring device on her ankle, no money or work permit, and a list of immigration check-ins and court dates piling up. Her children were frustrated, bored, unruly.

It was dawning on her that the caravan was only the first leg of a long and difficult journey.

Crossing into California, step by step

The caravan had been Estrada’s salvation, a way out of Honduras for herself and her four children that didn’t require the $15,000 smuggler’s fee.

She and her husband earned $8 a day baking bread in a firewood oven attached to their adobe house and selling it on the street in their town of Jícaro Galán.

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But last year a robber put a gun to her daughter Sheyla’s head on a bus and stole their money. A cousin, Jefferson, was shot 10 times and killed in August. And Estrada’s husband was growing increasingly violent, her children say.

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One night in October, Estrada and her children watched news of the caravan on television. The next day they boarded a bus to join it, carrying two clothes-filled backpacks and $40.

Estrada’s sister in Honduras alerted a grown niece in Atlanta that the family was on its way. The niece called other relatives in America, who debated which of them could afford to take in a family of five. A cousin in Texas backed out. A different sister in California demurred.

That left Francisca Estrada de Espino, 56, who lives in Bakersfield with her husband and his two sons and who hadn’t seen Estrada in many years.

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She watched the caravan trudging in the rain on television and wept.

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“How could my sister do this? It’s so difficult,” she recalled saying about the trek.

Estrada de Espino and her husband had crossed the border decades earlier, in an era when few migrants paid smugglers or landed in jail.

Rogelio Espino arrived in 1984 from Mexico to pick grapes and obtained a green card under the amnesty offered by President Ronald Reagan. He successfully applied for U.S. citizenship in 1997 after California’s governor, Pete Wilson — a Republican, like Reagan — attempted to crack down on undocumented immigrants.

“He did me a favor,” said Rogelio, a 54-year-old apartment maintenance worker.

Now a different Republican president was working to curtail immigration in every way possible.

Estrada had intended to cross the southern border at the legal checkpoint in Tijuana, Mexico, where advocates and lawyers were available to help and guide migrants. But food was scarce, daily crossings were strictly limited, and she ended up No. 1,520 on a dubious waiting list kept in a tattered notebook. One night, protesters threw rocks at the sports complex that was housing her family and thousands of others.

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She and the children were terrified of returning to Honduras. They heard whispers about a tiny beach not far from the stadium, where a rusty border fence vanishes into the Pacific Ocean. A taxi ride later, they were scouring the metal strips for weak spots, padding over the sand as if searching for seashells. Elen soon poked her tiny hands through a cracked metal sheet.

They crossed into California in late November and immediately surrendered to the Border Patrol. Officials released them to her sister and brother-in-law, who traveled by bus to get them since they couldn’t all fit in the Espinos’ battered blue Mazda. Together, they rode the bus back to Bakersfield, a city of 380,000 that sits 110 miles north of Los Angeles.

The rose-colored house, with a yard overflowing with scrap metal parts, was quickly engulfed in the chaos of two teenagers and two young children who had been on the road for the past six weeks.

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Espino installed an extra refrigerator and filled it with eggs, tortillas and pizza. His wife packed plastic containers with clothes from yard sales and Ross Dress for Less. They hung a hammock in the living room for Estrada, over a bed where her children could sleep. Nine people share one bathroom.

“I want to help them,” said Estrada de Espino, a housewife.

But there was no money for lawyers, and the long list of legal organizations Estrada had been given were all at least an hour’s drive away.Her hosts had little time to ferry her to appointments.

With the caravan, Estrada had been decisive. When her teenagers disappeared in the crowd for two days, she commandeered another migrant’s phone to find them. She lost the children’s birth certificates but had copies texted to her and printed in Tijuana. A gum infection cost her a front tooth, but it did not stop her journey.

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In California, though, her confidence faded. She had no money for Christmas gifts. The kids gobbled food she could not pay for. They stayed home all day, screaming or blasting music, as her sister pursed her lips in disapproval.

She couldn’t summon the courage to ask to borrow her sister’s phone to call nonprofits for help. “They’re feeding me,” she whispered. “How can I use their phone to call a lawyer?”

Waiting for a case worker

Her life, for now, was shaped by check-ins with Immigration and Customs Enforcement on a palm-tree-lined street in Bakersfield.

“How can I get a work permit?” she said she asked an officer on her first visit. Instead of an answer, she was handed the list of faraway lawyers.

She was told to stay home at her sister’s the following Monday, when a case worker with the federal contractor BI Inc. would visit to verify Estrada’s new address.

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Estrada was also told to keep her ankle bracelet charged, another way for the government to track her whereabouts.

In Honduras people had talked about immigrants who snip off the bracelets and run away. But Estrada and her sister wanted to follow the rules. “It’s better not to act incorrectly,” Estrada de Espino said.

Estrada rose early that Monday to make breakfast and keep an eye on the front window, jumping when someone parked outside. The case worker was supposed to show up sometime between 8 a.m. and 7 p.m.

The monitoring would eventually lead to an immigration court hearing that could determine the rest of their lives. But Estrada didn’t want to tell a judge or anyone else that in addition to gang violence, she was fleeing a husband who had threatened to kill her and their children.

“He was a good person when he wasn’t drunk,” Estrada said softly, sitting on her sister’s couch.

“She doesn’t like to tell the story about him,” 17-year-old Sheyla interrupted, sitting a few inches away. “When he came home drunk, we had to leave to find another place to sleep. He would come home and hit us.”

Tears welled in her mother’s eyes. But Sheyla’s gaze was hard. She said her father would point to a rifle he owned for killing livestock and say, “I’ll kill you with this.”

Sheyla and 14-year-old Eiro said the threats happened “many times.”

Estrada de Espino listened and handed her sister tissues.

“I don’t like people to know my problems,” Estrada said, clutching a teddy bear and watching the window.

At 12:12 p.m., a FedEx truck pulled up. At 3:08, the U.S. Postal Service arrived.

Sheyla cocooned herself in a blanket and texted her friends in Honduras; Eiro played an online soccer game. Erickson, 4, and Elen kicked soccer balls outside, stopping when they saw a group of schoolchildren pass. They hadn’t been in school since mid-October.

At 3:27 p.m., a neatly dressed young woman from B.I. Inc. arrived at the front gate apologizing and holding a phone with a dead battery. Estrada finger-combed Erickson’s hair and greeted her at the door.

After learning that a Washington Post journalist was with the family, the woman canceled the appointment without explanation and said she would come another day.

“Disculpa,” the woman said in American-accented Spanish. “Excuse me.”

The next day Estrada had another check-in with BI Inc. Again, she asked about working. The employee, she said later, told her she needed a permit to legally get a job but also acknowledged that many migrants work without one. The employee warned her to show up for her immigration appointments, Estrada said, and told her, the rest is “up to you.”

Bumpy start to a new life

The next day Estrada and her sister took Elen and Erickson to enroll in school, walking several blocks in the crisp air.

Elen, excited, wore a frilly black-and-white dress from the plastic container in the living room. She smiled when they arrived at the school, where the signs were in Spanish and almost everyone seemed to be Latino — either immigrants or U.S.-born. The only disappointment came when the clerk said Erickson was too young for kindergarten.

“The houses are so pretty,” Estrada said, gesturing to a small, tidy house with a pair of shade trees out front.

Even though her sister insisted she could stay as long as she needed, Estrada was anxious to start working, save money and get her own place. The sisters made plans to call a legal nonprofit, and Estrada asked whether she could find a job on a farm, maybe trimming grapevines for next season.

“I’ll learn what I have to learn,” Estrada said, “even if I have to collect garbage all day.”

Her family’s first immigration court hearing is scheduled for Jan. 31, but she received notices to appear in two different courtrooms, one of which is in a facility that immigration officials haven’t used since 2012. The other is in San Francisco, a 4 ½ -hour drive away.

She still needs to check in periodically with immigration officials and spend one afternoon each week at her sister’s house, waiting for the contractor to visit.

This month, her three older children started school.

Estrada missed being home for Christmas. She used to bring her mother fresh-baked bread, and a little money, every Christmas morning. She said she hoped to have the chance to go back to Honduras, at some safer time, and share the holiday with her mother again.

Returning home is a fantasy every immigrant shares, her sister told her, especially when they first arrive. But millions end up staying in America, with or without permission.

“That’s how it is,” Estrada de Espino said. “Once you leave, you don’t want to go back.”

Sarah Kinosian contributed to this report.