Prosecutors want to appeal against the two-year jail sentence for Oxford Eastern Bypass driver Angela Dublin because they think it is too lenient.
The Crown Prosecution Service has asked the Attorney General to apply to the Court of Appeal to increase the term after she was jailed for killing four people in last May's crash.
Last night, Dwain Haynes and Sam Hastings, parents of victims Marshall Haynes and Liam Hastings, welcomed the move. Mr Haynes called the sentence an insult to the families.
Dublin, 45, of London Road, Headington, was sentenced after she admitted causing the deaths of Marshall, Liam and Josh Bartlett, all 13, and Howard Hillsdon, 21, by dangerous driving.
Mr Haynes, of Greater Leys, said: "Once the case was sent to Crown Court, I felt justice would be done. But now my question is - why did a High Court judge issue a sentence which could have been dealt with the likes of speeding fines in a magistrates' court?
"The sentence is an insult to all the families who lost their loved ones and the boys' memories themselves. And what signal does the sentence send out to the rest of our society?"
At Oxford Crown Court this month, Mr Justice Crane said Dublin showed genuine remorse and anguish, and a lengthy prison spell would harm her physical and mental state.
Mr Haynes said: "Is my boy's life and three other innocent victims only worth a sentence more fitting of a shoplifter?
"For all the people who feel Mrs Dublin has suffered enough, I ask them this: when they kiss their children goodnight, ask themselves the question again would she have suffered enough if it were their child that was thrown 100ft from the boot of a car - yes, the boot, not a seat?"
Mrs Hastings, of Rivermead Road, Rose Hill, said she was pleased there was a chance the sentence could be extended.
"What she got is nowhere near long enough," she said. "She is going to miss one of her son's Christmases. We are going to miss at least 50 of Liam's. I know that even if the judge gives her 25 years, it's not going to bring Liam back, but she has killed four people and I think she should get at least double figures."
A spokesman for the Crown Prosecution Service said: "Papers have been passed to the Attorney General for him to consider whether it should be referred to the Court of Appeal as a potential unduly lenient sentence."
Attorney General Lord Goldsmith has until Monday, May 8, to decide whether to seek an appeal.
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