Rinehart’s estranged children, John Hancock and Bianca Rinehart, have launched fresh legal action challenging the ownership of Hancock Prospecting, which owns the $A10 billion Roy Hill project and a stake in the Rio Tinto-operated Hope Downs iron ore mine.

Lawyers for Hancock Prospecting had argued for the details of the case to remain private and there was a temporary suppression order in place, but that was dismissed yesterday in the Federal Court in Sydney.

A spokesman for Hancock Prospecting said the proceedings were an abuse of process and were another attempt by Rinehart’s two eldest children to air baseless allegations and avoid an arbitration they had agreed to.

"They are again using media for collateral purposes to extract benefits for themselves irrespective of the deeds they've repeatedly entered into and without any regard to many others,” the spokesman said.

"As a result, the Hancock Prospecting Pty Ltd Group is forced to have to waste precious time defending these extremely irresponsible, selfish and inconsiderate claims.

"I feel parents everywhere cringe at this scene, watching extremely privileged children suing to get even more money unearned by them, after their mother’s lifetime of hard work."

Rinehart’s younger daughter, Ginia, is publicly siding with her mother and last week called for the matters to be dealt with privately.