The ongoing legal feud among the Rinehart family members took a dramatic turn on Wednesday with the matriarch, Gina Rinehart who is Australia's richest person, issuing a public invitation for her four adult children to claim their share of the family trust.

However, John Hancock, her only son and one of Ms Rinehart's three estranged children, insisted on still removing her as head of the family trust because of her warning that the children would be bankrupt if the trust vested, which he disputed based on a separate financial advice.

Ms Rinehart based her warning on the advice of PricewaterhouseCoopers that the children are at the risk of financial ruin due to the large capital tax gains the transfer of money would cause. To avoid bankruptcy, she extended the vesting date to 2068.

The move led Hancock and two of his sisters, Bianca Rinehart and Hope Rinehart Welker to file a lawsuit against her mother to remove her as the fund's trustee for deception, manipulation and disgraceful conduct. One daughter, Ginia, sided with her mother in the legal battle.

David Russell, the barrister of Ms Rinehart, admitted the bankruptcy scenario would not have happened, which was taken as an opportunity by the children's lawyer, Andrew Bell, to question Ms Rinehart's fitness to head the family trust.

"That act provides a powerful insight into that person's suitability as a trustee," Fairfax quoted Mr Bell.

Mr Russell warned, "The mercurial destruction of (Ms Rinehart's) reputation as appears to be sought by their beneficiaries is the one thing that could seriously damage the trust assets . . . Bizarre does not begin to describe the extraordinary claims here . . . It is simply, simply a matter of spite."

In the same hearing, Ginia sought to deal with the lawsuit through mediation, but Justice Paul Brereton rejected her request because it has little chance of succeeding at this stage in the family's bitter court battle.

"Ginia had a most genuine interest in moving the case to mediation without further public ventilation of this very unhappy family dispute," Reuters quoted Francois Kunc, the lawyer of Ginia.

Mr Brereton reserved a decision on the estranged children's application to amend their statement of claim before the lawsuit goes to trial.

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