Bea Worton is challenging the decision to continue to call the park in Newry after Raymond McCreesh, an IRA member and hunger striker.
Her son Kenneth was one of 10 people massacred by the IRA at Kingsmills, south Armagh in 1976.
Three months later, McCreesh was one of three IRA members arrested in possession of a weapon which had been used in the massacre.
She is expecting to hear today whether or not she will be granted leave for a judicial review of decisions by both the Equality Commission and Newry, Mourne and Down Council to endorse the naming of the play park.
Larne FC suspends player John Herron after he was spotted on camera wearing ‘tiocfaidh ar la’ assault rifle top
Feile organisers asked if they have warned Wolfe Tones about leading young people in pro-IRA chants
Irish republican rebel band Wolfe Tones lead giant Belfast crowd in singing Up the Ra ‘on the same night as singing Give Peace a Chance’
Irish language group Kneecap accused of ‘grooming sectarian hatred’ with Feile mural
‘He needs to leave our club NOW!’ Strong reaction Larne FC’s John Herron being pictured in ‘tiocfaidh ar la’ gun top as club suspends him
Her son Colin told the News Letter ahead of the hearing that they were hopeful of a positive outcome.
“It is immoral and shameful to name a children’s play park after a convicted terrorist,” he said.
“It would be equally sickening to see anything named after a convicted loyalist murderer.
“Could you imagine the outcry if Hitler’s family put his name forward for the Nobel Peace prize? This is, we believe, in the same category.
“My family believe Raymond McCreesh was involved in the Kingsmills massacre.
“Those who took innocent life in this way can only be described as psychopathic killers and if they are still alive must face the full weight of justice.
“If they are dead then they cannot escape God’s perfect judgment.”
The Equality Commission, according to the applicant, should have found against the local authority and referred the matter to the Secretary of State.
McCreesh, from Camlough in south Armagh, was one of 10 IRA prisoners who died in the hunger strike in the Maze prison in 1981.
His convictions included attempted murder, conspiracy to murder, possession of firearms with intent and IRA membership.