The 37-year-old was charged with the murder of Matthew Healy, 6, on 8 or 9 February last week at Rathmoylan in Co Waterford.
Detective Sergeant David Shoer gave evidence of arrest, caution and charge.
He told the court that she was charged tonight and offered the opportunity to reply.
The court heard that after being invited to reply to the charge, she said: "No thank you."
Inspector Shay Keevans applied for a remand in custody, which was granted.
Judge Kevin Staunton remanded the accused in custody in prison until next Tuesday.
He also ordered that she be psychiatrically evaluated on arrival in the prison.
Matthew was found unresponsive in the back seat of the vehicle shortly after midnight.
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First responders desperately tried to save his life.
CPR was given at the scene before he was rushed to hospital, where he was later pronounced dead.
The remains of the tragic youngster, who lived in Ballygunner outside Waterford and was in senior infants at Faithlegg National School, have been released back to his father James Healy.
His funeral will take place at the Church of the Immaculate Conception, Watergrasshill in Co on Wednesday at 12pm.
It will be followed by a private service in The Island Crematorium Ringaskiddy.
Matthew’s death notice read: “Matthew James Healy of Watergrasshill, Cork and Ballygunner, Waterford died on the 9th of February 2024 unexpectedly, aged 6 years.
“Sadly missed by his heartbroken Dad James, grandparents, aunts, uncles, cousins and extended family, neighbours and friends.
“Fly with the angels. Family flowers only. Donations, if desired, can be made to Make a Wish Foundation www.makeawish.ie.”
Hundreds attended vigils to remember little Matthew in Waterford on Saturday.
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And in a statement on behalf of Mr Healy, released to the Irish Examiner, he thanked those who paid tribute to his son.
It read: “Matthew’s father, James Healy, expresses his deep gratitude for the several vigils that were held for his son Matthew throughout Waterford. He would ask at this sad time for privacy.”