Killers Molly and Tom Martens have begged a US supreme court to order a full retrial and uphold the overturning of their convictions for the murder of Limerick businessman Jason Corbett.
The daughter and father, who are serving 25-year prison sentences for the second-degree murder of Mr Corbett (39) in August 2015, have lodged a detailed submission to the North Carolina Supreme Court.
In the submission, which runs to nearly 100 pages, they argue that they did not receive a fair trial three years ago because key material they sought to introduce into evidence was not allowed by the judge.
They say this material was in support of their argument of self-defence and the state of mind Mr Martens was in that night.
The submission came one month after North Carolina prosecutors lodged their own legal argument for the supreme court to reject the court of appeal ruling and uphold the original murder convictions.
Father and daughter were convicted of battering the father-of-two to death with a metal baseball bat and a brick as he slept in his home in North Carolina in August 2015.
Tom Martens (69) is a retired FBI agent, while his daughter Molly (35), who was Mr Corbett's second wife, had a lengthy history of mental health problems.
Last month, officials for the North Carolina attorney general lodged a 96-page submission to the supreme court, seeking to have the court of appeal ruling overturned and the original second-degree murder convictions upheld.
The court of appeal ruling on February 4, by a majority 2-1 decision, granted the pair a full retrial.
Two judges found that decisions of the trial judge were potentially prejudicial to the defendants and may have undermined their ability to receive a fair hearing.
That appeal ruling was immediately challenged by the North Carolina district attorney's office, and the supreme court will now rule on either upholding the original conviction or granting a retrial, most likely for late next year or early 2022.
Both submissions revolve around two key elements of evidence that were not permitted during the original Davidson County Superior Court trial in July and August 2017.
Prosecutors have defended the decision of Judge David Lee to not allow into evidence statements taken from Mr Corbett's two children, Jack and Sarah, by North Carolina social services officials in the days after his killing.
Judge Lee did not allow these statements because they were directly contradicted by others made by the children weeks later on their return to Ireland from North Carolina.
The North Carolina statements were given after the children had been in the care of Ms Martens after the murder.
Tom and Molly Martens have both insisted they acted entirely in self-defence that night, despite the fact neither had suffered so much as a scratch or bruise at the scene.
Mr Corbett's skull was so badly crushed that a pathologist subsequently could not accurately count the number of blows inflicted.
Judge Lee also did not allow into evidence a statement from Mr Martens in which he recalled an alleged conversation with Michael Fitzpatrick, Mr Corbett's first father-in-law.
This statement was proposed for evidence on the basis it supported the defence case as to Mr Martens' state of mind at the time of Mr Corbett's death.
However, it was denied entry into evidence after it emerged that Mr Fitzpatrick, shortly before his death, made a sworn deposition to an Irish solicitor, having denied he had ever made any such statement.
A ruling by the North Carol- ina Supreme Court is not expected for several months, possibly not until early next year.