(CNN)The mother of two missing Idaho children has until Thursday to physically produce them to authorities, according to a court order served by police on Saturday.
Lori Vallow, the children's mother, and her husband, Chad Daybell, were served with a search warrant after authorities found the couple in Hawaii, the Kaua'i Police Department said in a news release on Sunday.
Joshua "JJ" Vallow, 7, and Tylee Ryan, 17, who have not been seen or heard from since September, were not with the couple, and there is no evidence that they were ever in Hawaii, authorities said.
Lori Vallow and Daybell fled their home in Rexburg, Idaho, in November, when authorities began searching for JJ and Tylee. It appears now that Vallow and Daybell have been staying on Kaua'i, though it is unclear how long the couple has been on the island.
Rexburg police believe the couple may have information that could help locate the children, and accused them of fleeing and not cooperating with the investigation.
CNN has attempted to reach Vallow and Daybell for comment.
On Saturday, Kaua'i police served Vallow with a court order to produce the children to the Idaho Department of Health and Welfare or Rexburg police within five days. Vallow could be subject to civil or criminal contempt of court if she doesn't comply, authorities said in a statement.
Then on Sunday, Kaua'i and Rexburg police searched the couple's vehicle and their townhome in Princeville, Hawaii, according to CNN affiliate East Idaho News.
Police did not say what, if any, evidence they found, and all documents related to the case are under seal, Rexburg police said in a statement.
The couple has not been charged and no arrest warrants have been issued for them in Hawaii.
"KPD's desire is to continue to assist the Rexburg police in whatever way we can with their efforts to locate the missing children," Kaua'i Police Chief Todd G. Raybuck said in a statement. "It's our sincere hope that the children have a safe return."
Relatives urge the couple to cooperate
Relatives of the couple and the children have pleaded for Vallow and Daybell to cooperate in the investigation.
Earlier this month, Matt Daybell, the brother of Chad Daybell, released a statement urging his brother to "come forward and cooperate with police."
JJ's biological grandparents, Kay and Larry Woodcock, offered a $20,000 reward for information on the whereabouts of JJ or Tylee.
"Please, just let us know where the kids are," Kay Woodcock said, in a plea to the children's mother. "It's not difficult. It will end all this, as far as the kids are concerned."
An attorney for the family, Sean Bartholick, released a statement to East Idaho News on December 23 saying that while he is in contact with Vallow and Chad Daybell, he does not have information about the children.
CNN has made multiple attempts to reach Bartholick but has not received a response.
Police discovered the kids were missing in November
Police determined the children were missing in late November -- four months after Vallow's estranged husband was killed in their former home state, Arizona, and shortly after she moved with the children to Idaho and remarried.
Police conducted a welfare check for JJ -- Vallow's adopted son with her late husband -- on November 26 at their home in Rexburg after relatives raised concern about not hearing from him since September.
During the welfare check, both Vallow and her new husband, Chad Daybell, told investigators the boy was staying with a family friend in Arizona, police said.
But police determined that he wasn't staying with a family friend. When police returned November 27 to execute a search warrant, investigators determined Daybell and Vallow had fled the home. And according to authorities, they didn't appear to have taken JJ with them.
Investigators also learned that Tylee hadn't been seen since September, though she'd most recently lived with Vallow and JJ in Rexburg.
The family has had a complicated year
The children's disappearance is part of a complex past 12 months for the family. Police have investigated two deaths in the couple's family in that time frame.
One of those deaths is that of Lori Vallow's estranged husband, who was shot and killed in July during a fight with Vallow's brother in their former home state, Arizona.
Details about the motive in the killing weren't immediately available. Vallow's brother was not charged in the case and died in December, according to CNN affiliate KIFI/KIDK. His cause of death has not been released, and an investigation is pending the results of an autopsy, CNN affiliate KNXV reported earlier this month.
Shortly after, Vallow moved with the children to Idaho and married Chad Daybell, who had links to a religious content website.
Vallow's former husband said she had "recently become infatuated and at times obsessive about near death experiences and spiritual visions," according to a petition for dissolution of marriage filed last February.
The second death authorities are investigating is that of Daybell's previous wife, Tammy Daybell, in Idaho in October. Though she was originally believed to have died of natural causes, Rexburg police ann