On Monday the Court of Appeal in Belfast ruled there was no doubt over the verdict that she killed Lesley Howell.
Stewart, 49, was jailed for a minimum of 18 years for the murders of husband Constable Trevor Buchanan, 32, and 31-year-old Mrs Howell.
The victims were found in a fume-filled garage in Castlerock, Co Londonderry in May 1991.
Stewart had planned to challenge the verdict that she was guilty of both murders as part of a joint enterprise.
But, after she was brought from jail into a courtroom packed with members of the two families, her barrister confirmed she was no longer appealing the conviction for killing her husband.
However, Jim Gallagher QC argued that Stewart only became aware of Lesley Howell's murder when her lover arrived at her house with the victim's body in his car.
He claimed there was no evidence she either aided in or knew in advance that the dentist was planning that killing.
Opening his case, the lawyer said: "We say in respect of the death of Lesley Howell that there was no actus reus (guilty act) on the part of appellant."
Stewart showed no emotion as senior judges announced their decision following a half-day hearing in Belfast.
I’m relieved that justice has been maintained for my mum.
Lord Justice Higgins, sitting with Lord Justices Girvan and Coghlin, said: "We have concluded that that application for leave to appeal should be refused.
"We have no reason to doubt the safety of this conviction."
Full reasons for the decision will be given at a later date.
Following the hearing, the only daughter of Colin and Lesley Howell, Lauren Bradford, spoke of her relief outside the court.
Police originally believed the pair had died in a suicide pact after discovering that their partners were having an affair.
They were, in fact, murdered before their bodies were arranged to make it look like they had taken their own lives.
It was nearly two decades later when Howell, 52, suddenly confessed to both killings.
He pleaded guilty to the murders in 2010 and is serving a minimum of 21 years in prison.
Howell also implicated his former lover in the plot and gave evidence against her at her trial.
In March 2011 a jury at Coleraine Crown Court found Stewart guilty on two counts of murder.
During the trial the prosecution alleged she knew about the plan in advance and actively facilitated her husband's killing by ensuring he was drugged and allowing Howell into her home.
She also disposed of evidence including the hose pipe used to gas their respective spouses, it was claimed.