They were located shortly afterwards and jointly charged with intentionally failing to comply with orders under the Covid-19 Public Health Response Act 2020.
The 12-year-old was not charged.
Having pleaded guilty to the charge in July, the mother and her teenage daughter made their respective cases at sentencing on Thursday afternoon.
The court heard the family tried to legally attend the tangi but their compassionate exemption application was declined, as was an alternative arrangement for the father's body to be brought to Hamilton.
"[This woman] couldn't believe the situation wasn't exceptional enough; so that the children could go to their father's funeral. His children were the most important thing to him.
"The defendant's motivation was to give her children closure and in desperation, when it looked like they were running out of time, she made the move to break out," the mother's lawyer Joseph Hamblett told the court.
The police prosecutor said while he sympathised with the woman's situation, denunciation and deterrence of such offence had to be front and centre in isolation escape cases.
Judge Sainsbury said there was an element of selfishness in the woman's offending; saying putting herself before the protection of the community "did not accord with tikanga".
The judge said New Zealand only had to look at Victoria to see the importance of adhering to Covid-19 restrictions, including complying with quarantine periods, in the face of personal hardship.
He accepted grief had likely clouded the woman's judgment and her negative tests given her a false sense of safety at the time.
However, he ended on a sentence of 14 days' imprisonment for the charge; an outcome that provoked shock and emotion from her daughter and other supporters in the public gallery.
One man sitting in the back of the court insisted he could pay a fine, pleading "she's got five kids", before saying "that's shameful" when he left the court.
The woman cried and hugged her daughter and other supporters before being led to the cells where she would be transported to prison.
Acting for the teenager, defence lawyer Michael Talbot said the 18-year-old had followed her mother's lead and had good reason to believe she did not have the novel coronavirus.
"At the time they left Brisbane there was no community transmission of Covid-19 in Brisbane and they had also passed their three-day test at the time they arrived.
"So she had no basis or reason to believe she had Covid-19 and perhaps a basis to believe she did not."
Judge Sainsbury said while this may have been the teenager's belief, it was "mistaken" as there were very good reasons the quarantine period was 14 days. Several people who have gone into managed isolation have returned positive tests at day 12, after returning negative tests at day 3.
However, the judge said the offending was at the lower end of the scale compared to someone who may break out of an isolation facility in an infected state.
The judge accepted the teenager had followed her mother's lead in a state of grief and discharged her without conviction.
"This was also a situation of very realistic grief. Your father had died suddenly and unexpectedly. I accept you had a particularly close relationship with him."
"I consider that the wish to see your father and say goodbye before his burial had an impact on overriding what might have been the sensible decision."
The maximum penalty for failing to comply with orders under the Covid-19 Public Health Response Act 2020 is six months' imprisonment or a $4000 fine.
