Ginia Rinehart and billionaire mother Gina lose bid to send Hope Margaret Hancock Trust fight to arbitration behind closed doors Ginia Rinehart and mother Gina Rinehart. GINA Rinehart's youngest daughter has failed in a last-ditch attempt to have the family's drawn-out trust fund saga moved behind closed doors. The decision by the Court of Appeal to dismiss Ginia Rinehart's bid to move the case, and the issue of who should be trustee of the multi-billion dollar fund, into arbitration means the matter is now set for a trial next week. Ginia, who has sided with her mother for almost all of the ugly legal battle, was appealing against an earlier court decision that refused to stay the proceedings. Australia's richest person indicated earlier this week "a desire to be discharged as Trustee" of the Hope Margaret Hancock Trust, citing the strain the long-running litigation has on her running of Hancock Prospecting. Gina Rinehart and daughter Bianca in happier times. But John Hancock and Bianca Rinehart, the two children from her first marriage, want the Supreme Court trial next week to test allegations of misconduct, deceit and dishonesty on the part of the mining magnate. The court heard earlier this week that the pair believe Mrs Rinehart "engaged in a deliberate strategy to mislead them" about the consequences of vesting the Trust on its original date in September 2011. Ginia Rinehart, 27, has previously admonished her siblings in publicly released emails for continuing to air the family's dirty laundry in public. The court heard a 2006 amendment to a deed indicated proceedings like the one currently before the court should instead be handled in arbitration, where it would remain confidential. Son John Hancock and Bianca are determined to have their claims aired in court. Picture: Michael Perini Source: News Limited But the appeal court today, stressing the "urgency" of giving judgment in Ginia's bid ahead of Tuesday's trial, said that claim "is not sufficiently arguable to give rise to or constitute a dispute under the Deed." Mrs Rinehart indicated to the court this week that she wants to "be heard" on her replacement during mediation with her children. The trial, scheduled to run for several days, will begin Tuesday morning.