Jayda, Maverick and Ember were recently filmed by teenage pig hunters, tramping across fields with their father and into the bush north of Marokopa in the King Country.
It apparently took police several hours to respond to what they called a "credible sighting".
Their father, Tom Phillips, has been on the run with them since 2021.
Earlier this week, the children's mother, known as Cat, told Mihingarangi Forbes the short interaction between the old pig hunter and a child she believes to be her daughter, Jayda - who asked, "Who knows we're here?" - was a cry for help.
Cat spoke exclusively to Mihi Forbes on RNZ's Saturday Morning about how she was coping, and said it had been "a lot of time pretending it's not happening".
"The first thing people always ask, is 'Is there any news?" Or ... 'How are your babies?' As if they're back. Like, I know? And it's just like, mate if my babies were back I wouldn't be here. I'd be with my babies."
Cat said she had had to deal with running commentary and opinions about the case and her parenting by strangers.
"I'm just dumbfounded. These people - they don't know Thomas at all, half of them have never met him.... None of them have met the kids. They're all just saying things. It's like they're all jumping on the most popular bandwagon.
Cat said she lived and worked in the King Country and had tried to stay out of public discussion of the case, despite people talking to the media and claiming to know her.
"People say they had met the mother, and then proceed to run me down. Like, I'm just gobsmacked - everybody just wants a little bit of fame or something, that's all it is to them... a little bit of 15 seconds [of fame].
"I wouldn't wish this situation on anybody, not even on my worst enemy. It's... wrong. That's all it is."
Cat - who has five children in total - wanted the New Zealand public to know she was a "good mum", and she had already raised two "amazing young women".
"They are an essence of me ... I taught them how to be, and that's what I had started with my little babies [Ember, Maverick and Jayda], and I would have continued on in that way, too."
The children had always been her priority, she told Forbes.
"They are who I am, and since they've been gone, I've lost my way. I'm not me. I'm lost. I'm lost without them.
"They were my world, my reason for being - and that was my only job in life, was my children.
"I feel like I've failed them miserably. I didn't fight hard enough. I didn't make enough noise.... I should have done more."
