The woman, who asked not to be named to protect her children, raced up the driveway and the car took off.
The 6-year-old told her that when she refused to get in the car, the pair made throat slitting gestures at her.
The accused driver and passenger were identified soon after the mother called police.
Auckland police spokeswoman Noreen Hegarty confirmed the pair gave statements. The man was processed for driving with excess breath alcohol.
The investigation was ongoing and further charges were possible.
Sergeant Peter Knight described the driver's behaviour as "alcohol-fuelled" and "in very poor taste".
"There is no excuse for adults to behave in such a way that they, whether intentionally or not, intimidate and frighten young children," he said. "Thankfully the couple at the centre of this incident was located quickly and are under no illusions about the impacts of their behaviour."
The girl's mother was disgusted by the incident.
Police had told her the people in the car said they could not remember trying to pick the girl up, and anything they may have done was a joke.
"You don't joke about asking a child to get into your car. You need to be pretty base-level strange to do something like that when you've been drinking," she said.
Her daughter was upset by the throat slitting, but knew not to get in a stranger's car.
"We are incredibly proud of her. She just thought it was ridiculous that someone she didn't know would ask her to get in their car. She said it was 'random'.
"What if she had gotten in the car though, or they had asked another child ... what if they crashed and killed the child?"
Her mother said the incident was scary, but saw it as a good opportunity to appeal to parents about the importance of teaching their children about stranger danger.
"It's real. Just because we live on Waiheke, it doesn't mean we can become complacent. It's a real issue and it has happened in our small beautiful community. We are not untouchable."
