Owen Scott, 29, of Heather Road, Fawley, Hampshire, was arrested after a car he was driving crashed into a pub near Penistone in August last year.
Four children were in the vehicle - two girls, aged seven and eight, and two boys, aged 21 months and nine months.
They were all taken to hospital in a serious condition with injuries "not all thought to be consistent with the collision", according to police.
At a previous hearing, prosecutors said Scott had used a hammer to inflict blows on the children in the grey Dacia Logan and had then driven deliberately at the front wall of The Travellers Inn, on the A629 between Sheffield and Huddersfield.
Scott, of Heather Road, Fawley, Hampshire, admitted four counts of attempted murder and one count of dangerous driving in January.
Michelle Colborne QC, defending, said Scott had "little or no memory" of events in the car.
Miss Colborne said her client had undergone a psychiatric evaluation and although he was found to be suffering from a "short-lived psychosis" at the time, this was not enough to amount to a psychiatric defence to attempted murder.
He is due to be sentenced at Sheffield Crown Court on Thursday.