The rest of the family have tested negative six times, and Derkzen said health officials have refused to re-test their daughter, who is asymptomatic and now on day 14.
"That is frustrating and doesn't make any sense because she is at the point that she is considered recovered. If she wasn't five she would be free to go.
"In 14 days we haven't got anything, and the chances of getting Covid are getting smaller and smaller.
"And we're now looking at another 11 days, which is hard for us to accept."
Derkzen and his wife were doing their best to keep their three young children entertained in the small space but they were "bored after five minutes of anything".
They had been allocated a space with two rooms and a small balcony, but were not attempting to isolate from one another.
"We have done effectively nothing to prevent getting Covid from her, and we've been tested six times already and we've been negative every time – we got our last result yesterday."
Derkzen and his wife were triple-vaxxed and he suspected his sons may have been infected in Europe last year, contributing to their immunity against the virus. They thought their daughter may have recorded a false negative in her pre-departure test.
Derkzen and his family had come to New Zealand for his wife's job as a critical healthcare worker.
"We are of course going to go on with this plan but our enthusiasm has been a bit tempered," Derkzen said.
"There is so much focus on the dangers of Covid and having to keep it out of the country, but there's absolutely no attention for the rest of the physical and also the mental health and wellbeing."
Derkzen said they had also been offered the option of splitting into different rooms, but decided this was not an option as they were moving to New Zealand as a family.
He said they had also asked for a vacuum cleaner, but been told it would be too much work to sanitise after it was returned, and would then have to be provided to all returnees.
"You're totally dependent on what they will or will not do for you," he said.
"Being stuck in this situation for such a long time with small children – it's tough on us, but of course also it's really tough on them."
In response to the Herald's questions about length MIQ stays, a Ministry of Health spokesperson said last week returnees who tested positive would have their isolation clocks "re-set", and stay an additional 14 days if infected with Omicron.
Anyone in the case's bubble is considered a "bubble close contact" and must have their isolation period reset for 10 days since their last exposure to the case.
Decisions on whether to split bubbles are made on a case-by-case basis, said the spokesperson.
"If the bubble close contact(s) remain in the same room as the case, their isolation period will reset from the day the case is deemed recovered.
"It is in these scenarios that some 'bubble close contacts' may have lengthy stays in a MIQF."
Twenty days is the maximum length of time a person can be kept in managed isolation under the Isolation and Quarantine Order 2020, but the spokesperson said officials retained the ability to require returnees to stay longer "if deemed clinically necessary from a public health perspective".
They acknowledged the inconvenience of extended stays in managed isolation but said it was important every precaution was taken to minimise the spread of Covid, especially the Omicron variant.
Derkzen was surprised the isolation period had not been reduced in light of Omicron's reportedly shorter incubation period.
"We're reading about what's happening in the rest of the world that they're shortening quarantine rules and the shorter incubation time for Omicron," he said.
"And we're wondering what's the view of New Zealand – it feels like they're driven by fear and not by logic."
Epidemiologist Michael Baker said the incubation period usually referred to the median time it took a person to become infected after being exposed to the virus.
"There's good evidence that [Omicron] has a shorter incubation period than Delta, which in turn is shorter than the ancestral strain.
"It was a bit unfortunate that the DJ in Auckland tested positive on day 9 – that hasn't really helped the cause for people hoping for a shorter incubation period."