At least 20 lawyers, including four senior counsel and another four barristers, have converged on the NSW Court of Appeal today as Australia's richest person, Gina Rinehart, continues her quest to keep a family feud private.

Mrs Rinehart, and her youngest daughter, Ginia, 25, are appealing against a decision of the NSW Supreme Court delivered in October last year, which found the dispute - over control of the multibillion-dollar family trust - can be thrashed out in court.

Mrs Rinehart says she and her four children signed an agreement in 2006 to resolve any issues that arise between the family members in confidential mediation or arbitration.

Three of her four children - John Langley Hancock, Bianca Hope Rinehart and Hope Rinehart Welker - have launched legal action against their mother, alleging "serious misconduct" in her role as trustee of the Hope Margaret Hancock Trust.

Their barrister, Andrew Bell, SC, says the case should be heard in open court.

Today's hearing, before Justices Tom Bathurst, Ruth McColl and Peter Young, is suppressed.