Owen Scott, 29, of Heather Road, Fawley, Hampshire, appeared before Sheffield magistrates.
He was remanded in custody to appear at Sheffield Crown Court.
Two girls, aged seven and eight, and two boys, nine months and 21 months, were involved in the crash near Thurgoland, Barnsley, on Wednesday.
South Yorkshire Police said the attempted murder charges arose from "injuries sustained by the four children which are not all thought to be consistent with the collision".
All four children remain in hospital in serious conditions, police added.
A man has appeared in court charged with four counts of attempted murder and dangerous driving after children were seriously hurt in a car crash.