The driver was hit in the chest and arm and the 18-year-old was struck in the neck.
Both teenagers remain in hospital.
Dalton, from Mount Druitt, in Sydney's west, was allegedly sitting on the back seat of the car during the incident.
He appeared in court via an audio-visual link from Surry Hills police station, where he was taken after his arrest.
Magistrate Michael Morahan formally refused bail.
Dalton is due to appear at Sydney's Central Local Court later this week.
Two other boys, aged 14 and 16, who are also alleged to have been passengers in the car appeared at Parramatta Children's Court on Sunday.
Both are charged with being carried in conveyance and cannot be named for legal reasons.
A 13-year-old boy also accused of riding in the car is due to appear at Bidura Children's Court, in Sydney, in May.
Senior detectives are conducting an internal investigation into the circumstances leading up to the shooting.
-AAP