Esther Davies, 43, from Rhosybol on Anglesey, has described the action as "unforgivable" and has called for answers for her, her family and the community.
Christ Church in the village of Rhosybol was closed for good in 1996.
The Church in Wales sold it in 2019 and plans to convert the property were approved in early 2021.
However, members of the community were unhappy with this decision over fears the 1875-built church was too close to existing gravestones.
The church is now privately owned, and the surrounding land is still available for the public to use and visit family graves. However, there are particular concerns that the plot of land sold with the church contained unmarked or unrecorded burials.
'We drove out looking for my sister when she was late home - the bypass was blocked off, I knew what had happened'
The community found that previous parish records showed around 20 infants were buried in the previous century without receiving gravestones.
In response to these concerns, in September, 2021, the Church in Wales said it was "committed to ensuring" that the surrounding land would remain as a "place of sanctity".
It told BBC News Wales at the time: "We have imposed restrictive covenants on the building and the land that has been sold and we will enforce these in the event of any breach in the future. We are concerned about claims made, since the sale, about possible unmarked or unrecorded burials in the area of the graveyard which has been sold. We are currently investigating the matter."
According to county councillor for Twrcelyn, Aled Morris Jones, however, it was subsequently discovered that there were "numerous" unmarked graves in the piece of land that had been sold.
Esther said that the news had left her family feeling "devastated".
The Church in Wales has now said it is is "extremely sorry" and that it had been a "mistake" to sell the land which was later discovered to contain unmarked graves.
It said it could not rescind the sale, but assured that development was prevented on the land and there was guaranteed access to every part, with a second pedestrian access to the unmarked burial site in the works.
The church has also offered to erect a memorial on the site.
Speaking to WalesOnline, Esther explained that the village of Rhosybol meant a lot to her and her family, who had lived there for generations.
She said: "I have both my grandmother and grandfather in that graveyard, I have my uncle, I have my great-grandmother, my great-uncle and this little baby there too".
Esther explained that in December, 1944, her late grandmother gave birth to twins - a girl and a boy.
Unfortunately the boy, named Richard Davies, passed away three weeks later.
Anglesey Archives' burial record, as seen by WalesOnline, showed that the infant's burial service took place at the Rhosybol graveyard on January 9, 1945, and was conducted by a Baptist minister.
Another document shows the arrangement of memorial stones in 1984, with each stone allocated a number which was then directed to an index of their family's details.
Richard was laid to rest in an unmarked grave, but Esther said she and her family had an idea of where his burial took place and believed it was on the piece of land that had been sold.
Esther said she felt the Church in Wales had not done enough to protect the unmarked graves.
"There's a few people in this community who have babies there," she said. "And although circumstances were different for everyone, Richard was not an illegitimate child, he wasn’t forgotten, he has a record."
She added: "This happened in 1945, there are just two generations between me and my grandparents, we aren't talking centuries ago here. So what angers me the most is that the Church in Wales haven’t even tried to find out the details of these graves.
"During my research in the archives, I found a plan for the church back in the 1980s - each stone got a number and each number could be found in an index which included names of the families of the loved ones that have been buried. Richard’s address matched that of my grandparents’ address. We have the same name - 'Davies' and we still live in Rhosybol - they could’ve easily paid us a visit and asked us ourselves."
She added: "I’ve never been so angry in my life. It's so upsetting. I think my grandfather was an individual who had a very strong faith. Records from the church showed that my grandfather used to help keep the cemetery tidy for free during his spare time. My grandfather died before I was born, so I never met him. But I think about how he must have felt, losing his son, and how conflicted he would've felt now - with his faith being so strong and keeping him going, and how much pain he would’ve gone through.
"It breaks my heart, that's what gets me the most, thinking about my grandparents. He didn’t ask for a penny for the work he did on the upkeep of the cemetery, and this is the thankyou he gets. They have sold his little baby."
Upon inquiries made to the Church in Wales, both Councillor Aled Morris Jones and Esther Davies said they had been told that an alternative pathway was currently being constructed to the graveyard for the public and families to use, with talks there could be a memorial for the infants of the unmarked graves.
But Esther has said she does not want a memorial. She said: "A memorial is not going to make this right. There are so many memorials that are put up for the wrong reasons and it makes it worse. I don’t want to go there and see a memorial that is going to remind me of what they have done."
However, Esther is not the only one concerned with future plans.
A meeting was held in the community to discuss the matter on Wednesday, March 13, where they shared their concerns with a representative of the Church in Wales.
According to Cllr Aled Morris Jones, there are now various conditions on the piece of land that has been sold to ensure that nothing happens to it. The county councillor of 20 years has now called on the Church in Wales to "consult with various families" affected by the matter.
He said: "The situation is very upsetting and very unfortunate. There has been a public meeting, but there has to be further consultation in the area by the Church in Wales to try and find out if there’s a consensus or charity support to place a plaque to commemorate all these unmarked graves for all the families that have individuals buried in the graveyard of Rhosybol church.”
He added: "The church should have never been sold considering that it was encircled by graves on all sides. Unfortunately, we must deal with the situation as it is. I wish to thank certain individuals amongst the community that have tried to deal with this situation since it came to light. The best step moving forward is for the Church in Wales to consult the various families on this matter."
Esther added: "I haven’t slept due to this and my aunty, who lost her twin and was with him for nine months, is devastated. I think of all the times we've asked about this situation, and wonder if they knew exactly what had happened and sold the land. I have tried to keep faith in all of this - mostly for my grandfather, I have tried. They had a duty of care for those babies and young children, and for us as the families. I want them accountable for what they’ve done."
In response, a spokesperson for Church in Wales said: "The Church in Wales is extremely sorry for the distress and anguish caused by the sale of Christ Church in the village of Rhosybol. We particularly regret that land was included in the sale which we later learnt contained unmarked graves. This was a mistake which has understandably been distressing for many people.
"We have been unable to buy the land back but can offer assurances that all the cemetery, including the land which was sold, is under a strict covenant which prevents any development and which guarantees access to every part. We are in the process of constructing a second pedestrian access to the unmarked burial site, not to replace the existing entrance but to supplement it. This will enable people to visit the site whenever they wish.
"We would also like to provide and erect a suitable memorial on the site of the unmarked graves. This proposal has been well received by the majority of those concerned and we are keen to gather the views and ideas of others in the community. Our senior clergy team in the Ministry Area is heavily involved and committed to ensure that whatever is done is carried out with sensitivity, respect and with local support.”