Police said Charlie Faumuina - known as "Big Grizzlie" by team-mates and fans - was not in the car at the time.
Kahui had alleged her father and Rachelle Faumuina got into an on-road altercation, honking horns at each other.
She said the argument continued until Rachelle - who is 38 weeks pregnant - drove away.
But a week on, it is just Kahui and her father who have been charged by police.
They are both due to reappear in the Manukau District Court on November 21.
A Counties Manukau police spokeswoman said the investigation was ongoing and no decision had been made about whether further charges would be laid.
Stories about the incident appeared on the day Faumuina was set to fly to the US with his All Black team-mates.
The powerful prop delayed his departure for a day, with coach Steve Hansen saying he was staying behind for 24 hours for "personal reasons".
Faumuina said from Chicago yesterday: "The matter is still before the courts so as you can appreciate I am not in a position to comment further but we would like to thank people for the support we have received."
Rachelle was unavailable for comment, but her brother Otto said the ordeal had been very "distressing" for her.
New Zealand Rugby Players' Association chief executive Rob Nichol confirmed that his organisation had provided some support for the Faumuina family over the past week.
He said the alleged incident, and its aftermath, had been a "challenging time" for the heavily pregnant Rachelle.
But, he said, "how they are dealing with [it] is outstanding.
"I think this issue has invaded their privacy probably more than most people would have expected or wanted," Nichol said.
"It's a reason why Charlie stayed back for an extra day - obviously this time is very special so if he could stay back to support Rachelle and be close to her [it] was well worthwhile.
"When you are going through tough times, it's family and friends you turn to and the Faumuinas have a lovely and fantastic network."
In April, Faumuina shaved off his trademark beard to raise more than $5000 for the Child Cancer Foundation.
He decided to have the close shave after running into his former primary school rugby coach whose son had cancer.
Added Nichol: "He's a quality guy - and it's not just the charities he's involved in.
"If you chuck him in with a group of kids he's awesome.
"Some of the stuff he has done for us is magical - you can't script it, you can't write it.
"He's a big guy with a heart of gold that just comes out.
"He has an infectious smile - the type of guy that people gravitate to with a great sense of humour. People like being around him."
