The Rinehart family feud that many Australians are following for its juicy details about the conflict involving the country's richest clan whenever there are court hearings, may soon be a close-door affair, if matriarch Gina Rinehart would have her way.

In October, there is another scheduled hearing with the New South Wales Supreme Court on the petition filed by Ms Rinehart's two estranged adult children, John Hancock and Bianca Hope Rinehart, to have her removed as head of the trust fund established by the family patriarch, Lang Hancock.

However, the mining magnate sought on Wednesday that the proceedings be stayed as she preferred that arbitration take place.

Initially, John and Bianca filed the case questioning their mum's changing the vesting date of $4-billion trust fund, but now the two are claiming she changed the constitution of their company, Hancock Prospecting, in 2006 to ensure she would not be removed as its trustee.

The lawyer of John and Bianca, Christopher Withers, said the alleged changes meant the children could not claim their shares unless they have the financial capacity to pay the capital gains tax, which they don't since they have been cut off from the family wealth since their estrangement.

Richard McHugh, the lawyer of Ginia Rinehart, the youngest daughter who sides with her mum, said the new allegations must be referred for arbitration since they fall under the terms of the deed.

Mr Withers asked NSW Supreme Court Justice Patricia Bergin, who is handling the case, to go on with the scheduled Oct 1 trial date even if she would favour arbitration. But the justice indicated the trial could not go on if the new pleading of the two children's allegations are covered by the deed.

However, Ms Bergin reserved her decision for now.

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