The woman appeared with her partner at Parramatta Local Court on Monday for the start of a five-day hearing on the charges.
The two assaults the 58-year-old woman pleaded guilty to occurred on Sydney's north shore in January and October 2021.
The two counts of intimidation, to which she has pleaded not guilty, involve a series of alleged incidents between January and August that same year.
Her 56-year-old partner, the former foster father of William Tyrrell, has pleaded not guilty to one count of assault and one count of intimidation over alleged conduct in November 2020 and October 2021.
The couple cannot be identified for legal reasons.
Prosecutors wanted to use statements and alleged threats the foster mother could be heard making in recordings from within her home to prove a tendency in her actions, the court heard.
But the woman's lawyer, John Stratton SC, opposed that plan, saying that if threats to smack a child were criminal conduct there would be offences occurring in "maybe every household in Australia".
In one of the recordings, a "smack, smack, smack" sound was heard and in another the alleged victim called the woman a "f***ing bitch", the court was told.
The couple had a long-running dispute with the child, who was upset they had brought another foster child into the home.
Threats were made about ending her time in foster custody.
The couple have applied for the remainder of the hearing to be held in closed court.
Mr Stratton said there were personal details about the alleged victim that were better off being suppressed.
In August, police dropped one charge against both the man and the woman of dishonestly obtaining a financial advantage or causing disadvantage by deception.
The couple said they would plead guilty to downgraded charges of procuring another person to make a bid on behalf of a seller at auction, resulting in a fine.
The pair paid a dummy bidder to bump up the auction price of their north shore home in December 2020.
Mystery surrounds the 2014 disappearance of William Tyrrell, who was three years old when he vanished from a property belonging to his foster grandmother at Kendall on the NSW mid-north coast.
Police have consistently sought answers in the years since his disappearance, including conducting a thorough search of the Kendall property in December 2020.
In June, lawyers for the foster mother called on detectives to respond to reports that criminal proceedings were being considered against her over William's disappearance.
Neither foster parent has been charged in relation to that case, however the mother was acquitted in 2022 of lying to the NSW Crime Commission about hitting another child with a wooden spoon.
The hearing before Magistrate Susan McIntyre continues.