Joanne Hayes and her family want the High Court to declare all findings or wrongdoings made against them by the Kerry Babies tribunal unfounded and incorrect.
The woman wrongly accused of murdering an infant over 35 years ago is hoping to vindicate the family's good name.
Her siblings Edmund, Kathleen and Michael are joining her in this application.
In 1984 Joanne Hayes, and members of her family, were arrested by gardai, following the discovery in Cahersiveen of a new born baby with multiple stab wounds.
The parents of that child, called baby John, have never been identified, nor has his killer.
Ms Hayes was accused of being the mother of baby John and murdering him, while her family were accused of concealing the birth of a child – all charges were dropped in October 1984.
A tribunal of inquiry was established in late 1984/early 1985.
Ms Hayes and her family say the tribunal contained numerous findings against them that were untrue, unfounded, not supported by any evidence, and were purely speculative.
They claim the tribunal wrongly found that the Hayes family lied to the tribunal, they were involved in an attempted cover up and had made false allegations against gardaí.
She claims the tribunal showed bias and a lack of fair procedures by allowing gardaí to imply she was "promiscuous" and "a woman of loose morals", and it made unfounded statements about her sexual history.
Ms Hayes also seeks a declaration that any findings of wrongdoing contained in the tribunal report were in breach of her constitutional rights.
Liam Reidy SC for Ms Hayes said the application was being made as part of ongoing discussions between the family and the state defendants.
In 2018, Ms Hayes received apologies over her treatment from both the then-Taoiseach, and current Tánaiste Leo Varadkar, on behalf of the State, and the then-acting Garda Commissioner Dónall Ó Cualáin.
The siblings have brought High Court proceedings against the Garda Commissioner, the Minister for Justice, Ireland and the Attorney General, seeking various declarations and damages.
The matter will return before the court next week.
