More of the Rinehart family's dirty linen will be aired in public following a decision today which allows a dispute over their billion-dollar mining fortune to be heard in an open court.

Bianca Rinehart and John Hancock are suing their mother Gina Rinehart, alleging "fraudulent concealment ... unconscionable conduct, undue influence and duress" in connection with her control of the giant Hope Downs mine in Western Australia.

Federal Court Judge Jacqueline Gleeson found today there should be a public trial about whether a number of agreements relating to the Hope Downs deed were "null and void".

Counsel for Gina Rinehart argued for the disputes to be heard in private arbitration.

The mining magnate submitted that her children signed a deed in 2005 which prevented them from suing her for allegedly wrongful conduct relating to the transfer of assets and shares from the $4 billion Hope Downs Trust.

However Christopher Withers, counsel for Bianca Rinehart, said his client was "pressured into signing the deed".

"There is no way the court can conclude the deed is enforceable because the disadvantage is so significant," Mr Withers said.

The case will return to court in late June.

The judgment came as the fortune of Gina Rinehart continued to slip in the wake of the collapse of the iron ore price.

According to the latest Business Review Weekly Rich List released today, she slipped from being the richest Australian to the fourth richest Australian with an estimated fortune of $6 billion.

At the peak of the mining boom Gina Rinehart's fortune was estimated at more than $20 billion.