Rogue Coalition senator Gerard Rennick was at the centre of yet more chaos in the Senate on Wednesday, as he sought a do-over of a vote blocking the government’s inquiry into the ABC because he missed a Tuesday night vote due to alleged “confusion”.

The opposition claimed the Senate had devolved into “shambles” as Senator Rennick continues to withhold his vote from his own government in his war on vaccine mandates.

But the Queensland conservative has had a minor win, as the government conceded to one of his main demands.

“The government has lost control of its own team,” Greens senator Sarah Hanson-Young said.

Labor, the Greens and the crossbench teamed up against the government on Tuesday night to force the suspension of a controversial Andrew Bragg-chaired inquiry into the ABC. The motion passed 23-22, with Senator Rennick and colleague Alex Antic following through on their pledge to not back the government in certain votes, over their opposition to vaccine mandates.

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But hours later, Senator Rennick returned to the Senate to claim there had been “confusion around pairing arrangements”, and that his vote should be counted after all. He asked that the motion be recommitted for a second vote.

Recommittal motions are usually reserved for instances of genuine misadventure preventing a senator from attending the chamber to vote. This could include an accident or injury, or a senator getting stuck in a lift or being in the toilet at the time of a vote.

Pairing arrangements are for senators who know ahead of time they cannot be in the chamber, such as if they are sick, on leave, or due to current COVID capacity restrictions on numbers in Parliament House.

Coalition frontbencher Anne Ruston said there had been a “mistake” and that the government wanted the vote taken again. This was fiercely opposed by Labor and the Greens, with Senator Hanson-Young – who had originally proposed the motion to halt the ABC inquiry – blasting the government push as a “stitch-up”.

“We have to take our jobs very seriously in this place … simply wanting to change the way votes were paired is really showing what a shambles this chamber is right now,” she said.

But by Wednesday, the government had backed down, deciding to let the original vote stand. Its leader in the Senate, Simon Birmingham, said he had decided there was not “an adequate example of misadventure” that would allow a new vote to be run.

Senator Birmingham. Photo: AAP

But Labor’s Senate leader, Penny Wong, railed against the government for allowing confusion over pairing arrangements for Senators Antic and Rennick, who had previously said they wouldn’t be voting with the government.

Senator Ruston later clarified that Senators Rennick and Antic had written letters asking that they formally be paired for non-legislative votes in future – meaning their number would be counted toward the government if a vote similar to the ABC motion occurred again.

Greens senator Nick McKim was also critical of the government’s initial recommittal proposal.

“Recommittals are not mulligans. It’s not like a second shot you get in golf because you shanked the first one,” he said.

Labor’s Kristina Keneally called it an “omnishambles”.

The confusion traces back to Senator Rennick’s pledge to withhold his vote from the government until Prime Minister Scott Morrison does more to oppose state vaccine mandates for workers. The federal government says it does not have much power to override state vaccine orders.

Senator Rennick said on Tuesday that he was meeting constitutional lawyers, as arranged by senior government ministers, to discuss the Commonwealth’s options.

While the substantive elements of his demands might go unsatisfied, the Queensland senator has had one part of list fulfilled. Senator Rennick, who has railed against alleged “vaccine injuries” in viral posts online, wanted the government’s compensation scheme for actual side-effects to kick in at a lower level of harm.

Senators Antic and Rennick. Photo: AAP

Previously, a person would have to incur $5000 of costs before the federal government’s indemnity scheme would kick in. Health Minister Greg Hunt announced on Wednesday that the threshold would be lowered to $1000.

Despite Senator Rennick claiming credit for the change, Mr Hunt said the government had been “considering this policy change for a number of weeks”. He thanked “all colleagues and stakeholders who have contributed”.

“The COVID-19 Vaccine Claims Scheme is designed to ensure that people who have suffered a recognised adverse event as a direct result of a COVID vaccine have rapid access to compensation,” Mr Hunt said.

“Reducing the threshold for access to the scheme from $5000 to $1000 will ensure more people can claim for eligible costs, including lost earnings and care costs, providing greater levels of comfort to those yet to make the decision to vaccinate.”

Senator Rennick has given no indication of when or if he will relent on his promise to withhold his vote. On Tuesday, he said he would be “flexible” with his demands.