Rachel's mother, Rose, today appealed to her son-in-law to "just admit what he has done".
"As long as he keeps on appealing, we have to keep on suffering and suffering. I can't put into words how it makes us feel; it's horrific," Rose said.
"I know with every fibre of my body that he is guilty.
"I wish that he would grow a conscience and just admit to what he has done.
"I'm hoping I'll be in my grave before he gets out," she added.
The wife-killer was granted legal aid by Mr Justice Adrian Hardiman at a hearing in the Court of Criminal Appeal. A lawyer for the State said there was no objection.
Any appeal should be based on alleged new or newly discovered facts that show a miscarriage of justice.
O'Reilly has always protested his innocence.
Rose Callaly said she hoped the family would continue to receive justice for Rachel. "Life should mean life," she said.
"I cannot accept the likes of him can get legal aid. My own opinion is if you are convicted of murder and found guilty, and you are allowed an appeal, you should be given only one chance to appeal and that's that. That should be it.
"I think it's disgusting. It just keeps bringing it all back again for us. It's ridiculous the public will have to pay for it.
"It's happening all over again for us. It gives you a pain in the pit of your stomach," she added.
Tragically, Rose and Jim Callaly lost another daughter, Ann, to cancer in October 2010.
"We have gone through hell from the time Rachel was murdered," said Rose.
"Something like this happens and it brings us back to those first days after the murder.
"To that time of uncertainty and that awful sick feeling in the stomach. There is no rest," she added.