Cai Xia Liao, 45, had been having an affair with the boy's Melbourne-based grandfather Brian Mach, 61, until he recently called it off, prompting her to allegedly tie and gag him after arriving at his home on Tuesday morning.
Police claim she then killed his grandson Alistair Mach, 4, whom he was babysitting, as the boy lay in bed, stabbing or slashing him with the shears in the head and neck. He also had deep defensive wounds to his fingers, hands and arms.
A neighbour alerted police after witnessing the second killing.
An out-of-sessions court hearing late yesterday was told Brian Mach had recently broken off a relationship with the woman. He was taken to hospital with minor injuries, police said.
Cai, who does not speak English, was charged with two counts of murder and one count each of intentionally causing injury and false imprisonment.
Her lawyer Sarah Pratt said Liao needed blood pressure medication and had suicidal thoughts.
The Herald Sun said more than 15 people closely connected to the Mach family turned out to watch the brief hearing, including the boy's stunned mother who sat holding a small teddy bear.
Many sat wiping away tears even before Cai was marched in flanked by security guards.
Family friend Diana Teoh, who had known Alastair since birth, told the newspaper he was "very bubbly, a very good boy".
"They (Alistair's parents) are trying to be strong for the rest of the family but they are definitely very devastated," she said.
Cai will return to court for a committal hearing on July 22.