Ms Ardern returned to parliament this week following her maternity leave.
During her absence, tension between politicians across the ditch has risen, with New Zealand's justice minister accusing Australia's deportation regime of lacking humanitarian ideals and Home Affairs Minister Peters Dutton hitting back.
More than 1000 Kiwis have been removed from Australia since stricter laws came into place in 2014 and New Zealand lawmakers have particularly been irked by the expulsion of their citizens on character grounds, especially those who have spent the bulk of their lives in Australia.
Added to that, Ms Ardern's deputy and stand-in, Winston Peters, accused Australia of breaching UN conventions, got into an exchange with former PM John Howard and, for good measure, called on Australia to change its flag.
But back in the captain's chair, the prime minister is not concerned.
"We have the kind of relationship that means we can speak frankly with one another and I really value that," Ms Ardern told AAP.
"I don't think that the fact we have different opinions on a few issues really holds us back."
New Zealand Justice Minister Andrew Little this week conceded Mr Dutton was unlikely to back down on the law any time soon, but said the air had been cleared between them.
Ms Ardern said that didn't mean the push was over.
"We will keep talking about citizenship, we will keep trying to protect the rights of New Zealanders who study, we will keep talking about deportation. None of it holds back the rest though," she said.
"The reason we raise it is because we hope for some change, but we also acknowledge it's their domestic policy and their right to set it."
She rejected the notion there was a growing gap between the two governments, saying neither's position on the matter had changed in years and that positive work was being done on other fronts.
As for Mr Peters' recent claim that Australia's flag was a copy of the Kiwi ensign and needed to be replaced, Ms Ardern said the argument would have to sit along pavlova and Crowded House on the pile of long-running trans-Tasman disagreements.
"I think you could add it to the list of things we have good banter about," she said.
And while there are no immediate plans, Ms Ardern said she was sure newborn daughter Neve would be accompanying her across the Tasman at some point.
"I need to probably give [Prime Minister Malcolm Turnbull] a chance to see her in the boots that he gave me."
