"She never received the help asked for," Justice Andrews said, describing the sentencing as "a very difficult exercise".
"You were overwhelmed," she told Pene.
"The sad fact is you made several attempts to get help."
Pene had hit Trent across the head while wearing a metal splint on her hand and wrist for a carpal tunnel injury.
The boy died on a mattress in the lounge of Pene's Edmund Rd home from a lack of oxygen after his spinal cord was constricted, restricting his breathing.
She had rung for an ambulance when she couldn't wake him and when examined, the toddler was found to have had previously broken ribs.
Throughout the two-hour sentencing yesterday Pene rocked as she sat in the dock, shaking and weeping.
Her supporters in the public gallery cried as Pene's circumstances were outlined.
Crown prosecutor Fletcher Pilditch said the case was tragic but called for a jail term.
The toddler had been placed with Pene and her partner when he was 5 months old and she had found herself under considerable stress.
Her cries for help "were unheard" by social workers, he said.
"What has to be weighed up is the conduct which led to the death of a child against the very clear mitigating circumstances of the offender.
"No one holds themselves more accountable than the offender herself ... but a young life has been unnecessarily lost as a product of violence."
In the past four years, six local children had lost their lives as a result of domestic violence, Mr Pilditch said.
"Assaults on young children are still occurring in this community ... this case sadly reflects this offending.
"This was a frustrated parent - tired, exhausted and possibly depressed. A violent outburst led to these tragic circumstances, an outburst born out of frustration."
Pene's lawyer Bill Lawson said she had found herself isolated from support when she and her partner moved to Rotorua.
Her own children, including the baby she had three months after Trent died, had since been removed from her care.
He urged the court to "not lose sight of humanity" in sentencing Pene.
"Jail is unnecessary. What we are dealing with is a woman regarded as a good mother, a mild-mannered individual. This is a tragedy."
Justice Andrews said sentencing "in this very tragic case" was a very difficult exercise.
"She never received the help asked for.
"I have to say, it is nothing short of tragic your calls to a social worker were not answered," Justice Andrews said.
Pene and her partner had argued the night she had slapped and shaken Trent when he woke.
In a letter to the court, Pene said her children, including Trent, had been her "reason for living".
Pene had taken full responsibility for her actions, Justice Andrews said.
"You were overwhelmed. The sad fact is you made several attempts to get help."
TO GET HELP
Plunket (freephone) 0800 933 922 CYFS (freephone) 0508 FAMILY (326 459) Barnardos (freephone) 0800 472 7368 Healthline (freephone) 0800 611 116 Youthline (freephone) 0800 376 633 or phone your midwife or doctor.
