They said separated and divorced parents must act in the best interests of their offspring, however bitter their disagreements in other matters. Instead, the woman "continued to express her disapproval, in discrediting terms, of her former husband", whom she used as a "scapegoat".
As well as imposing the 30,000 fine, the court ordered the woman to allow her former husband greater access to the three children, especially at weekends and during the school holidays.
Chiara Ingenito, a lawyer who was not involved in the case but is a specialist in family law, said the judgment was unprecedented.
"It's a historic sentence," she told the newspaper La Stampa. "Under Italian law, a court can intervene in cases like this with sanctions. But it's the first time that it has been applied in this way."
Francesca Zanasi, a lawyer who works on family disputes, said it was a warning to other parents not to go to war against each other through their children.
"The hope is that it will ensure that children are given priority - that parents prioritise their welfare, even if they are going through a divorce and are in conflict," she said.
The woman had tried to "demolish her former husband's relationships with his children", Carlo Rimini, a law professor from Milan University, told the newspaper. "This is known as parental alienation and in these cases judges should be severe."
The court in Rome had recognised that the woman had "obstructed the right of her former spouse to have a normal relationship with his children", Rimini said.