Sharon Collins, 46, of Kildysart Road, Ennis, was sentenced to six years in jail in October 2008 for soliciting a man to kill her partner PJ Howard and his two sons.
Her co-accused, Las Vegas poker dealer Essam Eid, was jailed for six years for demanding money with menace and handling stolen property. He is appealing his sentence.
The jury failed to agree a verdict on a charge of conspiracy against Eid and this morning Counsel for the State, Tom O'Connell, said it would not be standing over the conviction of Collins for conspiracy as it was 'logically unsustainable'.
The State was however standing over her conviction for soliciting a killer, he said.
Lawyers for Collins have asked the Court of Criminal Appeal to overturn the conviction for soliciting on a number of grounds.
Senior Counsel Brendan Grehan said there was an inconsistency in the jury's verdict and trial judge's charge had failed to give the jury adequate directions on the charge of soliciting.
He said the whole focus of the prosecution's case was on the conspiracy charge.
All parties in the case had agreed that the jury should be told it could not convict one of conspiracy without convicting the other.
He said the jury had not been given a clear direction by the judge. They had acquitted Eid of conspiracy but convicted Collins. Therefore, it was unclear on what basis the jury had approached the soliciting charge.
He said the trial judge should have given the jury a distinct explanation for the charge of soliciting and that the evidence to support that charge should have been pointed out separately.
What was required was separation of the two issues, he said, when in fact they were conjoined in the judge's charge to the jury.
Collins will also challenge her conviction on three other grounds including the evidence of Eid's accomplice Teresa Engle, who was a convicted criminal awaiting sentence in the US.
The appeal court will also be asked to consider evidence relating to the poison Ricin, which was found in Eid's prison cell and the evidence of an alibi witness.
The 32-day trial in 2008 heard that Collins used the name 'lying eyes' to search the internet for a hitman to kill her partner.
The trial was told she hated him because of his unusual sexual preferences.
The trial heard she also obtained a fake marriage certificate because Mr Howard's two sons, Niall and Robert, stood in the way of her inheriting his wealth.
Mr Howard gave evidence in support of Collins and had urged the judge not to send her to jail.
