Mrs Uncles said Walker's decision to appeal the sentence showed his lack of remorse.
"There are a lot of people who say he's got to live with that for the rest of his life," she said, but it was them who had a life sentence.
Stephen Palmer was seriously injured in the incident and Kayden French suffered a permanent head injury and will never fully recover.
Yesterday Walker's lawyer Eric Forster told Justice Helen Cull that Judge Bridget Mackintosh's sentence had not taken into account his client's remorse.
Mr Forster also said the six-month uplift for Walker's previous conviction for drink driving in 2014 was unfair.
Appearing for the Crown, Steve Manning said it was "very serious offending" for which the maximum penalty was 10 years' imprisonment.
Shortly before the fatal crash, police had spotted Walker driving dangerously on Pakowhai Rd and a member of the public had seen him driving at speeds of 120km/h in a built-up 80km/h area.
He had told police that before the crash he had been doing donuts and trying to drift. Mr Manning said what preceded the crash was "horrific driving".
The Government had doubled the maximum penalty for such offences in 2011 to reflect their seriousness, and Mr Manning said Walker was handed this sentence just nine months after a six-month disqualification for a previous drink-driving conviction had ended.
He said that when Judge Mackintosh had sentenced Walker she considered not only the earlier conviction but also his attitude to drink driving and speed, which he already had 70 demerit points for.
He had a blood-alcohol level of 218mg per 100ml - well over four times the legal limit.
Mr Manning said Walker's attitude was reflected in a sticker, which was still visible on the crumpled crashed car, which read: "If I die speeding don't cry because I was smiling" - a tribute to The Fast and the Furious actor Paul Walker who was killed in a car crash.
He said Judge Mackintosh had granted him a discount for his youth.
Mr Forster said while his client had contacted the victim's families following the crash, he was told to "stay away" while the investigation was ongoing.
He said his client's decision to holiday with his fiance in Hawaii soon after the crash had left a "sour taste" in the victim's families' mouths. But he went because the holiday was already organised.
Justice Cull, who had read the victim impact statements, said they showed Walker had shown little remorse.
The Crown supported this, saying remorse was not shown in the early stages after the crash and the statements showed a "real beef" remained with the Uncles and French families.
Mrs Uncles said the appeal showed Walker could not accept his punishment. "He's been in prison four months and my son has been dead nearly a year and we are just waiting for it all to stop."
Justice Cull reserved her decision.
