Rudolph applied for bail which was opposed by the police. Davis made no application for bail. Their next appearance is on January 30.
Detective Senior Sergeant Rhys Johnston said police were not looking for anyone else in relation to the home invasion.
Earlier police said two women knocked at the 92-year-old's door asking for petrol, then assaulted her with a weapon, searched her home and stole property.
The victim, who was injured and extremely shaken by the attack, was admitted to Bay of Islands Hospital and discharged late the following day.
During the incident, a number of valuable possessions were allegedly stolen from the woman's home, including jewellery and her wallet, containing bank cards.
Police recovered the stolen items last week.
The most important item to the woman was also recovered, a calling card which was given to her by her late husband more than 75 years ago.