Interim name suppression was upheld by Justice Sinclair, who also declined media applications for filming and photographs.
The man is charged with one count of kidnapping the victim, who has name suppression.
Represented by Kelly-Ann Stoikoff, he pleaded not guilty and was remanded in custody until next month.
The 28-year-old is charged with two counts of kidnapping victim and one charge of threatening to kill.
Represented by Anabel Maxwell-Scott, she also pleaded not guilty and was remanded in custody until next month.
The 42-year-old is charged with kidnapping and entered no plea.
Represented by John van der Zanden, her application for bail was opposed by police.
Justice Sinclair declined her bail and she too was remanded in custody until next month.
Following the disturbing discovery of the victim last week, police used a photo of the woman's distinctive rose tattoo with the words 'Mum' and 'Dad' attached to it to appeal for help to identify her.
By the end of the week, her family were by her hospital bedside but the woman remained in a serious but stable condition in Auckland Hospital, where she was airlifted to by the Auckland Westpac Rescue Helicopter.
The trio appeared together in the dock while name suppression and media photo applications were discussed.
Five male guards flanked them.
The two women were dressed in casual clothes and appeared to chat and joke with each other, and try to engage the guards in conversation.
The man was wearing a dark grey shirt, and stood with his head hung and shoulders hunched.