While Kidwell is reluctant to banish the pair, there remains the possibility they could serve their penance on the sidelines during the World Cup pool games against Samoa, Scotland and Tonga, before returning for the business end of the tournament.
"We'll come up with a solution," said Kidwell.
"I have (spoken to the pair) and they're extremely remorseful, sorry for their actions and this is out of character, but I'm still extremely disappointed and gutted.
"I have to think about that as a captain but they have to live and breathe what we're trying to build there with the Kiwis and ultimately we've got a real big goal there at the end of the year and that's to win the World Cup.
"I want to make sure that I have the collective thoughts from the NZRL, from the team leaders, and part of my job is going to be to work closely with the clubs to monitor them."
Former test skipper Simon Mannering is the best candidate to reclaim the captaincy, having overseen the Kiwis throughout their 2014 Four Nations triumph and the 2015 Anzac test victory.
Five-eighth Kieran Foran, having led New Zealand twice in 2013, also has the right credentials, having also captained Parramatta last season before his career and personal life spiraled out control.
Both Mannering and Foran may have reservations about taking the job on, but question marks hang over the suitability of other first-choice players Shaun Johnson, Issac Luke and veteran prop Adam Blair, who started off the bench in Canberra, to fulfill the role.
Kidwell has also been forced to defend his own position at the helm, with the off-field drama adding weight to the argument he is not up to the job, having managed just one win - a 17-16 escape against England - from six starts since he succeeded former coach Stephen Kearney last September.
Last Friday's 12-30 Anzac test flogging in Canberra was the fourth defeat to Australia under his watch, while an 18-18 draw against Scotland is another black mark on his record.
"At the moment I am the coach," said Kidwell. "And I'm going to be here and I'm going to make this right.
"When the going gets tough the tough get going. And I'm here."
Listen: Kiwis coach David Kidwell on the Radio Sport Breakfast