John and Margaret Lawson and their children Theresa and Mark have demanded a meeting with the Catholic Archdiocese of Glasgow to discuss what they describe as a noisy and unsightly turbine in St Peter's Cemetery in Shettleston.
And the couple are being backed by local councillor Frank McAveety.
But so far they say they have had no response from the Archdiocese.
As the Evening Times revealed in August, the family was devastated after the turbine was put up next to Kevin Lawson's grave.
Kevin was 19 when he was killed in Tollcross on March 8, 2003. George Monaghan, 27, from Partick, was jailed in February 2004 for 11 years for his culpable homicide.
Since then the grave has been a place of solace for his family but the erection of the "monstrosity", which buzzes, horrified them. Theresa Lawson said the family are Catholics who take their faith seriously, but they now feel they have been "slapped in the face" by the diocese.
She said: "Every letter we have sent, we have got a general reply, the same reply every- one else gets. I do not feel they are interested in it.
"They are of the frame of mind 'it has been put up so deal with it'."
Councillor McAveety has also written to the Archdiocese of Glasgow to ask it to review the decision on where the turbine is located.
He said: "I am disappointed that is seen as an appropriate location for a turbine, but the Archdiocese has gone through the planning process.
"I am happy to make representations on behalf of the family. Ultimately, I am driven by their concern.
"The family has been through a tough time and this hardly helps."
The Lawsons plan to present the Archdiocese with a petition bearing at least 740 signatures opposing the 40ft turbine. The family expects more signatures to come.
Theresa, 36, said they wrote to the Archdiocese to request a meeting nearly two weeks ago.
They say they have not yet had a reply, but are hopeful they can ask questions about the turbine.
Theresa said: "Ideally we want it removed altogether but if we are not going to get that, better they have it moved a bit back from the gravestones – we would take that.
"We feel like things are moving in the right direction and hopefully we will get the meeting."
A spokesman for the Archdiocese of Glasgow said it had contacted the family.
He said: "The installation was made after due consideration of the sensitivities of all visitors, to ensure that St Peter's will be maintained to its current high standard well into the future."