The man said he was supposed to come from Tauranga to collect the children but he was sick and had asked their mother to pick them up.
In the third video, in which fast food could be seen on the bonnet of the car, the man said the children were left in the car like "animals".
He said the kids were starving and goes on to say "New Zealand Police you should be proud of yourselves - I ain't".
The videos have attracted thousands of online comments, most condemning the actions of the police.
However, Eastern Bay of Plenty area commander, Inspector Kevin Taylor, said the woman had been arrested for breaching bail conditions which included not associating with some of the children she had in her car.
In a written statement Taylor said when the woman had been arrested, police offered to drop the children to a family member who lived nearby but the woman would not agree.
She arranged for a family member in Tauranga to come and get them instead and he took three hours to arrive.
Police then suggested the children could wait for the family member inside the station, but the woman would not agree to this.
She insisted that the children would be looked after by the 18-year-old in the group and told them to stay in the car and not enter the police station.
"Police take our responsibilities seriously and made every effort to ensure the safety of these tamariki."
The woman, aged 30, is due to appear in Hamilton District Court on September 20 facing three charges of assault of a child.
The man who posted the videos could not be reached for comment.