Supreme Court Justice Patricia Bergin in Sydney has dismissed Rinehart’s request. The news service said the judge’s written ruling wasn’t immediately available to allow some commercially sensitive information to be omitted from the public version of the decision at Rinehart’s request.

The case raises the issue to what extent can disputes over trusts, particularly when large sums are at stake, can or should be held in private to protect beneficiaries and other interested parties.

John Hancock, Rinehart’s only son, and her eldest daughter Bianca sued to remove their mother from managing a family trust, claiming she breached her duty, failed to act honestly and has a conflict of interest. Gina Rinehart is the world’s 38th richest person with a net worth of $19 billion .

The dispute may still go to mediation before a trial next month, the judge said.

Christopher Withers, Hancock’s lawyer, said at the hearing that he wouldn’t object to mediation as long as it occurs in parallel with trial preparation. Bruce McClintock, Rinehart’s lawyer, proposed three days of mediation to be held from 23 September to 25 September. Bergin tentatively agreed to delay the start of the trial by a week to 8 October.