The 30-year-old is accused of killing Adeline Rigney-Wilson and her children, Corey, 5, and Amber, 6, whose bodies were found at a house at Hillier, north of Adelaide, on Monday.
Peet was brought into the court in handcuffs and was wearing a blue jumpsuit.
He appeared to have some minor facial injuries but made no comment during the appearance.
Defence Counsel Andrew English told the court that his client would not be seeking bail with Magistrate Brian Nitschke remanding Peet in custody to appear in the Adelaide Magistrates Court by video link on August 9.
When the bodies of Ms Rigney-Wilson and her children were found, police described the deaths as domestic related.
But they declined to reveal how the trio were killed and no details were given in court.
Several family members attended the hearing but made no comments.
Earlier, the dead woman’s mother, Donna Rigney, described the 29-year-old as a beautiful woman who had problems with drugs, something that had strained their relationship.
They had not spoken for about four months.
“She was a good mother. She growled, but it doesn’t matter because you’ve got to pull your kids into line and that’s how she did it,” Ms Rigney said.
“She got mixed up with the wrong crowd but she always made sure her children were right.”
Ms Rigney said she did not know her daughter’s partner and did not want to know him.
It is believed Ms Rigney-Wilson and Peet had only been living together at the Hillier property for a matter of weeks.
Barossa Local Service Area officer-in-charge Chief Inspector Alby Quinn said the nature of the crime was very traumatic.
“This does appear to be domestic-related and we are not looking for any other further persons in relation to this incident,” he said.