Ms. Vallow and Mr. Daybell eventually turned up in Hawaii but without the children, and in late January, the Kauai Police Department said it had served her with a court order to take her children to the Idaho Department of Health and Welfare.

The deadline came and went, but neither Ms. Vallow nor her children appeared.

On Thursday, the Kauai police said that they had arrested Ms. Vallow in Princeville, and that she would attend a hearing on the island “where she will have an opportunity to waive or fight her extradition to Idaho.” Mr. Daybell was not arrested.

In court on Friday, a judge set bail for Ms. Vallow at $5 million and scheduled another hearing on her extradition on March 2.

Idaho court documents supporting the charges against Ms. Vallow said that when the police searched her and her rented Ford Explorer in Kauai, they found Tylee’s bank card, which was still active and had been used since Tylee went missing months ago.

The Rexburg police also discovered that Ms. Vallow sent an email in July asking the facility in Arizona that had trained her son’s service dog to find another family for the dog “due to a change in life circumstances,” the court documents said. The training facility picked up the dog on Aug. 30.

Mr. Daybell’s parents also told the police that Mr. Daybell and Ms. Vallow had told them that Ms. Vallow was “an empty nester,” according to the documents.

Was a religious organization involved?

Relatives of Ms. Vallow and Mr. Daybell have suggested that the couple’s religious beliefs isolated them from their family members.