After a torrid fortnight consumed by Deputy Prime Minister Barnaby Joyce’s personal life – culminating in his resignation as Nationals leader on Friday – the federal government has been trying to change the subject.

As part of that strategy, Treasurer Scott Morrison and Minister for Revenue and Financial Services Kelly O’Dwyer visited a business in O’Dwyer’s Melbourne electorate of Higgins on Wednesday.

Standing in front of the blue-and-white logo for Helloworld Travel in Ashburton, Morrison talked up the tax cut the government has legislated for small businesses. “As a government, we are just getting on with the job,” he said. “There’s a lot to do. We are getting about it and particularly supporting small businesses like Helloworld.”

What Morrison apparently didn’t know until later was that the publicly listed parent company of the Helloworld brand he was spruiking is 26 per cent owned by the Liberal Party’s honorary federal treasurer, Andrew Burnes, who is also the company’s chief executive. Burnes’s wife, Cinzia, is also on the board.

Former treasurer and now ambassador to Washington Joe Hockey owns a smaller stake in the company, whose chairman is also the executive chairman of Myer, Garry Hounsell, who just sacked his Myer chief executive.

Morrison’s spokesman told The Saturday Paper he had no prior knowledge of the Helloworld connections. He said O’Dwyer’s office had set up the visit around the local franchisee.

O’Dwyer’s spokesman says her office was aware of Burnes’s involvement in Helloworld but that the visit was focused on the franchise business, which was “100 per cent owned and operated” by their local host, franchisee Daniel Addicoat.

Nevertheless it was the parent company’s logo and name they were effectively advertising.

Morrison’s spokesman acknowledged that the apparent lack of communication – and consideration of how it might look to be spruiking the brand of a senior party office-holder – could be described as sloppy.

While the prime minister’s code of conduct precludes ministers from offering assistance to a company, there is a caveat upon which they routinely rely in using businesses as backdrops: “except as may be appropriate in their official capacity as minister”.

Prime Minister Malcolm Turnbull’s departure for the United States after dispatching of Joyce on a week’s personal leave had not, at time of publication, provided the circuit-breaker for which he had hoped.

So it becomes just a bad look and another untidy dimension to what has been a very untidy start to the year for the Turnbull government.

Prime Minister Malcolm Turnbull’s departure for the United States after dispatching of Joyce on a week’s personal leave had not, at time of publication, provided the circuit-breaker for which he had hoped.

Joyce’s interview with Fairfax newspapers alongside his new partner, Vikki Campion, was an attempt to have the political attention move on. But in canvassing even further the reaction to his split from his wife of 24 years, Natalie, and his decision to form a de facto relationship with his now-pregnant former media adviser, it had the opposite effect. The added pressure of sexual harrassment allegations from a woman in Western Australia late in the week proved too much, and Joyce announced on Friday he is stepping down from the leadership of the Nationals and hence the deputy prime ministership to go to the back bench.

In his Fairfax interview, Joyce maintained that interest in his private life was unwarranted. “This should be a very simple story – a bloke whose marriage broke down is in a relationship with another person and they are having a child,” he said. “Now it seems to have gone into some sort of morality discussion. That’s between me and my God. I can understand how Natalie can be angry, absolutely, but how it’s other people’s business, I don’t know.”

Yet it was Joyce’s own moral arguments in opposing same-sex marriage and the subsidising of the cervical cancer vaccine Gardasil – he said it could make young women promiscuous – that has contributed to the deputy prime minister’s own travails and gave his earlier refusals to step down so much attention.

Joyce continues to insist he did not breach the ministerial code of conduct in having the affair with his then adviser, in having her employed by two consecutive colleagues after he was forced to recontest his seat over dual citizenship, or in then accepting the gift of a rent-free apartment in which the pair could live in Armidale in his electorate.

Some senior colleagues believe Turnbull inflamed matters in his own interview with 3AW radio host Neil Mitchell on Monday.

Turnbull told Mitchell there had been “a degree of greyness, moral ambiguity” about sexual liaisons between parliamentarians and staff.

Would he sack someone who engaged in it?

“Oh, yes, certainly – absolutely,” he said. “Well, I’d expect them to resign. I wouldn’t expect I’d need to sack them.”

Turnbull said he had always taken this view about “relations of this kind by ministers”.

“I’ve always felt they were inappropriate. I know many have thought they were entirely private matters and you can understand why relationships like that would be better off coming to an end privately.”

Mitchell accused Turnbull of inconsistency, asserting he knew about Joyce’s affair for some time before addressing it.

“No,” Turnbull said, after a number of long, stumbling pauses. “That’s an assumption. You’re saying that I knew about it. It was not ever confirmed to me by Barnaby Joyce.”

Joyce now says Turnbull never asked him. “He never asked any direct questions and, to be honest, if I believed it was private, I wouldn’t have told him either,” Joyce said in his newspaper interview.

Joyce was enraged at the personal nature of Turnbull’s attack in announcing amendments to the ministerial code, especially his declaration that “nothing good” could come of an intra-office affair, when in this case a baby was the result.

He and Campion told Fairfax they were concerned their child would be seen as “somehow less worthy” than others.

“I don’t want to say have sympathy for me,” Joyce said. “I just want people to look clinically at the facts and basically come to the conclusion he is not getting a gold star for his personal life, but he has made a commitment, he is with her, they’re having a child, and in a 2018 world there is nothing terribly much to see there.”

Nationals MP Andrew Broad took to Twitter on Thursday to note the death of American evangelist Billy Graham and send his own party – and leader – a message.

“When wealth is lost, nothing is lost,” Broad quoted the late preacher as having said. “When health is lost, something is lost; when character is lost, all is lost.”

He said these were “telling words for the leadership of the National Party”.

The man touted as most likely to succeed Joyce, Veterans’ Affairs Minister Michael McCormack, sowed doubt about his ability to take over with a series of ill-judged television interviews this week in which he failed to either fully endorse Joyce or confirm that he would challenge.

Some Liberals and Nationals believe both Joyce and Turnbull were at fault in twice re-igniting what had become a dying issue, sending it into its third week of media coverage and now threatening not one job but two.

Several senior ministers – while furious at Joyce for his behaviour – believe Turnbull’s intervention was foolish and has made things worse.

Unconfirmed rumours of other current and past affairs involving serving ministers, among others, continue to abound in Parliament House.

Many in the government and beyond are noting that Turnbull’s ban on ministers having sex with their staff pointedly does not extend to ministers having sex with other colleagues’ staff.

But having drawn the line there, while also describing it as a moral issue, Turnbull may face more complicated questions in future.

His redrafted statement of ministerial standards went up on his department’s website the day he announced the change, with a new prime ministerial foreword attached.

“While this new standard is very specific, ministers should be acutely aware of the context in which I am making this change and the need for them always to behave in their personal relations with others, and especially their staff, the staff of other ministers or members of the Australian Public Service, with integrity and respect,” Turnbull’s statement now reads.

Coincidentally, Turnbull’s ban was announced just as the latest fortnightly Newspoll was going into the field. The poll showed it had received the strong public support he had hoped, something he sees as vindicating his decision. But his party’s polling went backwards again. And colleagues are despairing at the government’s inability to get back to its policy agenda.

Just before Turnbull took off for Washington, conservative Liberals executed an effective pincer movement on the thorny issues of immigration and national security.

Former prime minister Tony Abbott ramped up his calls for a cut to immigration, demanding the intake be slashed by almost 50 per cent. Separately, Home Affairs Minister Peter Dutton took to the podium at the National Press Club to advocate reinstating tougher provisions to strip dual-national foreign fighters of their citizenship, despite previous legal advice that it could be unconstitutional.

Abbott’s intervention provoked a strong backlash from a string of ministers, including current and former immigration ministers, Dutton and Morrison.

Dutton said he wanted to bring in young, skilled migrants who would be paying tax and “helping build our nation”.

At the suburban Melbourne news conference at Helloworld, Morrison said Abbott had never raised such a substantial intake cut with him as immigration minister. He said migration was good for Australia’s economy, to which Abbott responded that Morrison had been “captured by his department” because Treasury always wanted more migrants.

Amid all this brawling, Turnbull returns to Australia for the resumption of the House of Representatives next week. The Senate will hold its regular estimates committee hearings, where Labor, Greens and crossbench senators are relishing the chance to interrogate ministers.

All is going swimmingly in the government, it seems. Hello, world. Nothing to see here.