Owen Scott will now serve an extra decade behind bars after judges increased his sentence from 13 years and 188 days to a minimum of 24 years.
Scott admitted four counts of attempted murder and dangerous driving after he attacked his three children and a step-child with a hammer before driving his car, with them inside, into a wall at 92mph.
The 29-year-old, of Heather Road, Fawley, Hampshire, was jailed for life at Sheffield Crown Court in February but Solicitor General, Robert Buckland QC MP, had referred the case to the Court of Appeal, arguing that the original minimum term was not long enough.
Lord Justice Treacy, sitting with two other judges, said: "In our judgment the facts of this case demonstrate a case of particular gravity which justified this.
"Four young lives have been grievously affected, their mother's life has been blighted and the level of harm which has been done is very high indeed.
"It follows from that analysis that the sentence imposed below was unduly lenient."
Speaking after the hearing, Mr Buckland said: "Four children’s lives have been devastated by Scott’s actions, and the physical and mental scars will stay with them for the rest of their lives. I am pleased that the Court of Appeal has agreed to increase Scott’s sentence to properly reflect the seriousness of his crime.”
Scott, who claims to have no memory of the incident, was arrested after his car crashed into the Travellers Inn at a remote location near Penistone, South Yorkshire, in August last year.
In the weeks before the incident, he developed paranoia, put down to a temporary psychosis caused by his long-term recreational cocaine and cannabis use.
All four children, aged between nine months and eight years at the time of the crash, were left with "life-threatening and life-changing" injuries as a result of multiple blows delivered by Scott.
Medical reports indicate they will have lasting psychological damage and cognitive impairment, and one child will need a wheelchair for life.
Speaking after Scott was first jailed, Detective Chief Inspector David Stopford, of South Yorkshire Police, said the scene of the crash was so horrific that officers who attended were "astounded" to find the children alive.
He said at the time: "This has been, without doubt, one of the most harrowing cases I've worked on."