For five months, no one has been able to find 7-year-old Joshua “J.J.” Vallow or his sister, 17-year-old Tylee Ryan.

The mystery of their disappearance deepened amid their mother’s abrupt move from Idaho to Hawaii with a brand-new husband, the suspicious deaths of multiple people connected to the couple and rumors of their involvement in a doomsday cult. As questions swirled and the bizarre case drew international headlines, the children’s mother, Lori Vallow, refused to cooperate in the search, authorities said, despite knowing “either the location of the children or what has happened to them.”

On Thursday, with the siblings still nowhere to be found, their mother was arrested in Princeville, Hawaii. The 46-year-old woman was charged with two counts of felony desertion of a child, along with misdemeanor charges of resisting and obstructing an officer, solicitation of a crime and contempt, the Kauai Police Department said in a statement.

“We are hoping against hope that Tylee and J.J. are out there somewhere and will be reunited with their other family members at some point,” Kauai prosecuting attorney Justin Kollar said at a news conference Friday afternoon local time.

Her arrest was welcomed by the grandparents of the missing boy, whose request for police in Rexburg, Idaho, to conduct a welfare check on him led to the discovery that he and his sister had vanished and tipped off the ever-expanding investigation. Authorities later learned neither had been seen since September.

“We are relieved,” grandmother Kay Woodcock told EastIdahoNews.com. “We are ready for the next step which for Lori is: where are the kids? Where are the kids? Where are the kids?”

Vallow and her husband, Chad Daybell, have denied wrongdoing. A statement released in December by their attorney, Sean Bartholick, said the two “look forward to addressing the allegations once they have moved beyond speculation and rumor.” Bartholick did not respond to a request for comment on Vallow’s arrest.

Police began investigating the couple in November, after Joshua’s grandparents became concerned about not hearing from him. When authorities showed up at Vallow’s townhouse in Rexburg, she said Joshua, who has special needs, was staying with a family friend in Arizona.

“Chad acted as if he didn’t know Lori very well,” noted an affidavit obtained by the East Idaho News site.

Authorities called the family friend, who told them Joshua had not been at her home for months. She added that Vallow and Daybell called her and asked her to tell police that the boy was with her.

But when the officers returned to Vallow’s home the next day with a search warrant, they found it abandoned. Most of her clothing was gone. They visited a unit she rented at Self-Storage Plus and discovered belongings that appeared to belong to the children: a blanket with pictures of Joshua, another with pictures of Tylee, a backpack with Joshua’s initials, children’s clothing, a photo album, bikes, a scooter and toys that appeared appropriate for a young boy.

The case soon grew more complicated, spanning multiple states. Authorities in Fremont County, Idaho, began to question the death of Daybell’s first wife, Tammy, which came in October, just two weeks before he married Vallow. Her death had been considered natural at the time, but her body was exhumed and an investigation opened after the children disappeared.

“Those are the two pieces of this,” Fremont County Sheriff Len Humphries told Fox 13 in Salt Lake City in January. “And how they’re related we’re not quite sure, but we do believe they are related.”

Vallow’s former husband Charles, who had told a divorce court that she believed she was a reincarnated deity, was shot and killed by her brother in a July dispute that remains under investigation in Chandler, Ariz. The brother, Alex Cox, died in December; an autopsy report is pending. Chandler police told local media they have questions for Vallow about the death of her previous husband.

Daybell and Vallow may have bonded over shared beliefs. He penned self-published apocalyptic novels aimed at Mormon audiences; she believed herself a god sent to Earth with the mission of preparing people for the second coming of Christ, according to divorce paperwork filed by her previous husband. The two appeared together on podcasts distributed by a company devoted to preparing people for biblical end-times, which has since distanced itself from them.

They were married in Hawaii in November. In wedding photos obtained by ABC News, they wore purple leis and wide smiles while embracing on the beach. By then, Joshua and Tylee hadn’t been seen for weeks.

During their investigation, authorities learned through phone records that Tylee had joined her mother and Cox on a day trip to Yellowstone National Park on Sept. 8. A photo of the girl at the park was discovered on Vallow’s iCloud account, the affidavit said, time-stamped with that date. It is “the last time we can find any record of [Tylee] being with Lori Vallow,” a Rexburg police detective wrote.

Joshua was last seen at his school, Kennedy Elementary, on Sept. 23. The next day, Vallow told school administrators he would no longer be attending and she planned to home-school him. She told neighbors and a babysitter he had gone to stay with his grandmother.

Rexburg police have expressed grave concerns about the children, saying in a December update on the case that they “strongly believe that Joshua and Tylee’s lives are in danger.” The couple told one person that Tylee had died a year before her father, the update noted. Daybell told his parents that Vallow was an “empty-nester,” according to the affidavit.

“It is astonishing that rather than work with law enforcement to help us locate her own children, Lori Vallow has chosen instead to leave the state with her new husband,” Rexburg police said.

Her arrest came after she failed to comply with a court order to produce her children for authorities in Idaho. The deadline was Jan. 30. Vallow is now being held at Kauai Community Correctional Center on $5 million bail. After a hearing in March, authorities expect she will be extradited to Idaho to face charges.

Daybell was seated in the audience during Vallow’s Friday court appearance, clad in shirt and tie, and maintaining a flinty expression during the short proceeding. Hours later, Kauai police chief Todd Raybuck told at the afternoon’s news conference that he’s not aware of any criminal charges against Daybell, who he said is still free to “move about as he wishes.”

The affidavit said the children have never been seen with Vallow and Daybell in Hawaii, where the couple has been surveilled by police and hounded by reporters whose questions they ignore. Their condo contained no items that suggested a child lived there, though Kauai police found the children’s birth certificates, Tylee’s bank card and Joshua’s iPad in Vallow and Daybell’s possession while executing the search warrant.

A review of Vallow’s financial records, the affidavit added, has found no evidence of anyone providing for the care of Joshua or Tylee since they were last seen in September.

Reis Thebault contributed to this report.

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