When Malcolm Turnbull’s cabinet discussed changes to the way child-care subsidies were to be paid, Peter Dutton declared an interest: the family trust run by his wife, which has investments in child-care centres.

However, despite acknowledging his family’s interest, The Saturday Paper has confirmed that Dutton did not absent himself from the room during deliberations on several occasions. Some of his ministerial colleagues believe he should have.

Dutton does not deny being present for such cabinet discussions. In response to questions from The Saturday Paper, a spokesman said: “The minister has always declared any conflict of interest in accordance with cabinet rules and absented himself whenever necessary.”

The revelation comes as Dutton battles a series of leaks about his ministerial discretion in issuing visas at the request of former associates.

Other ministers have said Dutton did not offer to step out when child-care policy was being discussed.

Police are investigating the leaks, which have also formed the basis of a Senate inquiry this week into whether the minister exercised his ministerial powers inappropriately.

Dutton strenuously denies any ministerial wrongdoing, including any misuse of discretionary intervention powers in immigration, and says he is the subject of a smear campaign led by disgruntled former Border Protection staff.

But at the same time, he faces more questions over his family’s investments, both in relation to a potential conflict of interest and whether such an investment might rule him ineligible to serve in parliament.

According to the federal Cabinet Handbook, once a minister has declared an interest during a cabinet meeting it is up to whoever is chairing to either excuse the minister or “expressly agree to his or her taking part”.

It is not clear whether then prime minister Turnbull expressly agreed, but other ministers have told The Saturday Paper Dutton did not offer to step out when child-care policy was being discussed.

Separate cabinet sources say this happened on “several” occasions when cabinet discussed changes to the way child-care funding was to be distributed to eligible centres.

One minister says that after Dutton declared his interest he proceeded to offer comment on the child-care industry “from the point of view of operators”. Another minister endorses that recollection.

The statement of ministerial standards lays out in more detail what ministers with potential conflicts of interest are required to do.

The statement says cabinet ministers must declare any potential conflict between their governmental roles and any investments they or their families hold.

The standards say ministers should “make appropriate arrangements to ensure that any conflict of interest is avoided”, which may include divesting themselves of the interests, transferring the relevant decision-making responsibility to another minister, or placing the investments in a blind trust.

Alternatively, they might make other arrangements “to the satisfaction of the prime minister” that avoid the potential for a conflict of interest.

“If, for instance, a minister is required by these standards to dispose of an interest, the simple transfer of the interest to a family member via a nominee or private trust under their control is not an acceptable form of divestment,” the ministerial code says.

Dutton’s wife, Kirilly, is the director of a family trust that holds investments in two child-care centres.

Peter Dutton has declared the investments on the register of parliamentary interests.

Disclosure standards and distancing requirements are generally higher for investments not placed in a blind trust – a trust set up to independently administer a person’s private interests to expressly avoid conflict of interest.

The statement of ministerial standards says that, in relation to a blind trust, where “a reasonable apprehension of a conflict of interest arises”, the minister must declare any interest to both cabinet and the prime minister and either transfer his or her decision-making responsibility or “absent themselves from Cabinet consideration”.

During what turned out to be Malcolm Turnbull’s last question time as prime minister, on August 22, the Opposition asked him whether Dutton had excused himself from the Turnbull cabinet’s child-care deliberations.

With Dutton sitting on the back bench that day, having quit the ministry after his failed first leadership bid, Turnbull promised to consult the cabinet secretary and report back to parliament as soon as he had the answer.

“His eligibility to sit in parliament is now completely in doubt.”

But after that question time ended, he never spoke at the dispatch box again.

Dutton has insisted previously that he absented himself from some child-care discussions of the preceding Abbott cabinet.

Sky News commentator Peta Credlin, who was chief of staff to the then prime minister, Tony Abbott, supports him in that declaration.

Credlin volunteered on air two weeks ago that Dutton had not participated in discussions on child-care in the Abbott cabinet.

“It’s well known about his interests in child-care centres,” Credlin said “… He recused himself from any conversations we ever had in policy terms.”

Dutton’s family investments have also prompted questions about whether the child-care centres’ receipt of more than $5 million in government-paid subsidies might threaten his constitutional eligibility to sit in parliament.

Dutton has two sets of legal advice declaring he has no eligibility problem under section 44 of the constitution, which rules out anyone with “any direct or indirect pecuniary interest in any agreement with the Public Service of the Commonwealth”.

Constitutional experts are divided on the issue.

The solicitor-general, whose advice the government sought before Turnbull was deposed, said Dutton was probably “not incapable of sitting”, but that only the High Court could say for sure.

This week, The Australian Financial Review published details of a letter dated in March this year, which outlined what it describes as a funding “agreement” between the Commonwealth and one of the Dutton family’s child-care centres to hire a special teacher for an autistic child.

Having received its own legal advice previously that suggested Dutton might be constitutionally ineligible, Labor’s shadow attorney-general Mark Dreyfus said on Thursday that the Opposition would now have “no choice” but to ask parliament to refer the Home Affairs minister to the High Court for adjudication.

“His eligibility to sit in parliament is now completely in doubt,” Dreyfus said.

Dutton has rejected that and also hit back over his use of discretionary powers within the immigration portfolio, as a Senate inquiry investigates the circumstances of two interventions he made in 2015 to overturn separate deportation orders for a French and an Italian au pair after personal appeals from contacts.

Dutton previously told parliament he did not have personal ties to the people who had made the requests but they have since been revealed to be a former Queensland police colleague, Russell Keag, and the chief executive of the Australian Football League, Gillon McLachlan. Keag is alleged to have inquired on behalf of an Italian au pair arriving at Brisbane Airport, while McLachlan asked for help to stop the deportation of a French au pair who was on her way to visit his second cousin’s family in South Australia.

Greens MP Adam Bandt has accused Dutton of misleading parliament – something the minister denies.

Late this week, Dutton engaged in a full-blown public attack on the man he blames for the media storm over his discretionary powers, the former Border Force commissioner Roman Quaedvlieg, who was sacked earlier this year over a personal relationship with a staff member.

Late on Wednesday, after the Senate inquiry completed its one-day hearing into the issue, Quaedvlieg wrote to the committee expressing surprise that the Home Affairs Department and the Australian Border Force had not contacted him before their officials gave evidence.

Quaedvlieg said he felt “duty-bound” to tell what he knew, writing that he had received a call from Dutton’s chief of staff – who he named as Craig Maclachlan – on the day in mid June 2015 that the Italian au pair was detained in Brisbane.

Quaedvlieg said the chief of staff claimed to be ringing on behalf of “the boss”, Dutton.

“He told me that the Minister’s friend, whom he referred to as ‘the boss’s mate in Brisbane’, had encountered a problem with his prospective au pair who had been detained at Brisbane Airport by immigration officials due to an anomaly with her visa,” Quaedvlieg wrote.

He said Maclachlan had asked him to investigate and when he reported back that the young woman was being held ahead of deportation for a suspected breach of her tourist visa, the chief of staff asked: “What needs to be done to fix this? Can the boss overturn it?”

Quaedvlieg said he explained the minister’s intervention powers and then played no further part in the incident or the decision.

Dutton issued a statement late on Thursday blasting Quaedvlieg and effectively calling him a liar. Dutton said Maclachlan was not working in his office at the time and nor was he working for the department.

Dutton also said he had not asked any staff member to call Quaedvlieg and none had done so.

“Mr Quaedvlieg is bitter about the loss of his job and it has been concerning to hear allegations about Mr Quaedvlieg’s engagement with the media and Labor over a long period of time,” Dutton said. “But the fabrication of evidence to a Senate committee takes his behaviour to a disturbing level.”

He said he had asked Quaedvlieg’s successor, commissioner Michael Outram, to offer his predecessor support “to address his personal or mental health issues”.

Earlier on Thursday, on Sydney’s Radio 2GB, Peter Dutton accused Quaedvlieg of having been behind the leaks against him.

“There’s a disaffected former senior Australian Border Force official who leaks this information out,” Dutton said.

“Good luck to him, if that’s what he wants to do. He is obviously very close to the Labor Party.”

Quaedvlieg’s letter to the committee insisted he had received many calls from journalists seeking information and had “assiduously declined to accept these invitations and have not placed any information onto the public record”.

Dutton’s subsequent statement said it would be up to the Senate as to whether the former commissioner had breached any rules in providing what Dutton said was false evidence.

On Thursday evening, Quaedvlieg issued a statement saying he rejected the assertion he fabricated evidence. He did not address the confusion over who rang him. “I stand very firmly by the description of the events as I have recollected and outlined,” the statement said.

He said he would “attempt to correlate them” to the date of the Brisbane case “or alternatively to another Brisbane case which occurred at a later date and which may not yet be in the public domain”.

And he hit back at Dutton’s suggestions he might be unstable.

“I urge Dutton to desist from personal attacks and casting aspersions over my actions, motivation, integrity, reputation and mental health,” Quaedvlieg said, adding that he had anticipated this reaction.

“He would serve and respect the system of parliamentary democracy much better if he engaged with its mechanisms through civil discourse and through the appropriate mechanism.”

In his letter to the Senate committee, Quaedvlieg said he sought to claim parliamentary privilege over its contents because “while some will applaud my decision to clarify the public record others will take a dimmer view”.

That, it seems, was an understatement.