Australian Border Force is preventing a baby who was born in immigration detention and is still there seven months later from being baptised in a church, according to the family and a Catholic priest.

It is the latest in what supporters claim is exceptional treatment of Huyen Tran and her seven-month-old daughter, Isabella, who was born into detention in Melbourne, and comes as new details emerge about an attempt to deport Tran while she was seven months pregnant.

A United Nations body is now examining whether Australia is breaching its human rights obligations by holding Isabella in arbitrary detention.

Tran and her daughter are housed under guard in a section of Melbourne’s immigration detention facility, and Tran has sought to have Isabella baptised in a local church.

According to Father Peter Carrucan, a Catholic priest who has been visiting the Melbourne detention centre since 2010, Australian Border Force has repeatedly refused or ignored the request.

“The detention centre is a very unsuitable place for the celebration of baptism,” Carrucan told Guardian Australia.

“The room that’s allocated to us is books and chairs and desks and things, so it’s totally unsuitable to invite people to come and share in the celebration.”

“The church is only five minutes away from the detention centre and in the past we’ve used it for a number of baptisms – not so much for children, mainly for adults.”

Carrucan said they previously had a nicer room to hold masses in the centre but were moved to the classroom-like area without explanation.

“When I asked the manager why he said: ‘Because I said so.’”

Tran is Vietnamese and sought asylum in Australia by boat with her brother in 2011, at the age of 21. A Catholic, she claimed she faced religious persecution in her home country, but an assessment determined she was not entitled to protection.

The Asylum Seeker Resource Centre says Tran has not had the opportunity to be fairly assessed and has limited legal options because she arrived by sea.

They are not permitted to live in the community with Tran’s husband, who lives in Australia on a 457 working visa and is unable to sponsor his wife.

Tran was previously in community detention but absconded in 2014 when several friends were deported.

In 2017 she met Paul, and fell pregnant in November, but was returned to detention.

A psychiatrist has found Tran suffers depression and Isabella is showing signs of anxiety.

In late January Tran was told she was being deported, and two days later was put on a plane, only to be taken off again without explanation.

She was 32 weeks pregnant and suffering severe anxiety and gestational diabetes.

Lawyers for Tran had attempted to get a legal injunction before she was put on the plane but it was unsuccessful. The department had relied on a letter from an IHMS doctor advising she was safe to fly.

Guardian Australia can reveal a second letter from the same doctor revising his position never made it to the judge, and wasn’t discovered by Tran’s team until four months later.

Since then she has remained in detention in Melbourne, and has applied for ministerial intervention in her case, to allow her and Isabella to live with Paul on his 457 visa – not as permanent residents.

Earlier this month Tran was woken early and told to dress for court, but not told why. She feared a second deportation attempt. Documentation showed ABF had known about the court date – which was to hear the judgment of her federal court case – for at least a week but hadn’t informed her or her caseworkers and representatives.

Guardian Australia has been told ABF has sought to get travel documents for Isabella without the permission of her parents, prompting fears they are preparing to deport both mother and child together, away from Isabella’s father.

ABF did not respond to questions about the travel documents.

Tran has alleged there have been numerous other arbitrary moves to stop her seeing people or keep her informed, including a number of instances when she wasn’t able to see scheduled visitors.

Last week Tran said she had a visit booked in for 1.30pm, and was required to be picked up by guards and taken to the visitor centre at the main detention centre.

“I was still waiting at 2 o’clock, and I said it was so long a time, my visitor is waiting for me,” she said.

“They said oh it’s 2 now, it’s too late, I can’t bring you.

“I have my baby, I get up from my house, it’s hard to get everything and come here and then you say I can’t go. I get upset.

“All the times you change the law like this, it makes me crazy. I lost my visit.”

Tran said she was also stopped from going to Carrucan’s afternoon church service recently.

“I said I’ve been in detention one year now and every week I go to church. Today I go to mothers group but I want to go to church because it’s more important for me,” she said.

Tran’s husband Paul visits every afternoon. ABF told Guardian Australia Tran had the same services as others in the detention centre, with the addition of a maternal and child health nurse.

The department describes Isabella as being “housed in an alternative place of detention”. It is a “residential-style facility” in which Tran can self-cater and cook.

“That really is a lie, they are in detention,” said Carrucan.

“Huyen told me she was [previously] allowed out to do some shopping, but she has to go with about three or four security officers.”

Guardian Australia understands it has been some time since Tran was able to leave the centre for anything other than court, and a lack of socialisation is having a detrimental effect on her mental health.

Last week the United Nations working group on arbitrary detention – which advises the Human Rights Council on which Australia successfully petitioned to sit – received a submission on Isabella’s case.

“[Tran] can’t come and go whenever she wants, she’s got guards around her,” said lawyer Alison Battisson.

“It’s completely unclear to me how they could maintain that [she is not in detention] as a distinction. It’s an argument of form over substance.

“It’s to do with the duress Huyen must have felt she was under to sign permission for Isabella to stay with her in detention while she was breastfeeding. No mother should have to make that choice.”