Police said the aggravated burglary charge was in relation to an alleged incident at the same address earlier on the night of Te Kani's death.
The defendants also faced five alleged assault charges with persons unknown against other people at the address on the night of the murder.
There are two joint charges each of wounding with intent to cause grievous body harm, one each of injuring with intent to injure and assault with intent to injure.
The defendants were earlier granted interim name suppression and appeared before Judge Christopher Harding. No bail applications were made.
Crown prosecutor Justine Sutton, appearing for police, said the continuation of name suppression was opposed because publication could lead to more information from the public to help police with the homicide investigation.
However, she asked Judge Harding to suppress the police summary while police inquiries continued.
But lawyer Tony Rickard Simms sought continued name suppression for his client until his next court appearance, arguing there was a risk to the accused's right to a fair trial if his name was made public.
Rickard-Simms also submitted that publication may put his client and his family's safety at risk and identification was a key factor in the prosecution case.
Pini's lawyer, Norman Tekanawa-Gwynne, told Judge Harding his client did not seek the continuation of name suppression.
Judge Harding lifted the suppression order for Pini but said that despite the Crown's opposition he found "compelling reasons" to continue the suppression order for her co-defendant, at least until his next court appearance.
He also suppressed the summary of facts and remanded both defendants in custody to next appear in Tauranga High Court on July 13 by audiovisual link.
Judge Harding offered his condolences to a large number of Te Kani's family seated in the packed public gallery and thanked them for being so respectful during the hearing.
Police have said further arrests and charges could not be ruled out.
Anyone with information is asked to contact police on 105 and quote file number 220515/3688. or provide the information anonymously to Crime Stoppers on 0800 555 111, or on the Crime Stoppers website.