Sanjeev Chada, 43 and from Ballinkillen in Co Carlow, attended a brief hearing at Harristown Court on Friday morning - just hours before the joint funeral of Eoghan, 10, and Ruairi, five, in their hometown.
An all-Ireland alert - the first of its kind - had been sparked after the two boys were reported missing from their home on Sunday night.
But on Monday afternoon, gardaí attending the scene of a one-vehicle collision near Westport in Co Mayo found the boys' bodies in the boot of the car.
Their father was arrested after being released from hospital.
In court, a Garda Inspector applied for the accused to be remanded in custody for two weeks, but Chada's legal team expressed concerns and inquired about psychiatric help.
Judge Conal Gibbons directed appropriate medical treatment for Chada, but not a psychiatric report.
Chada, who first appeared in court on Thursday night, was remanded in custody and is now due back before Harristown Court on 16 August.
The two young boys, who were so close they shared a bed, were buried side by side following their funeral mass in St Laserian's Church in their home town of Ballinkillen on Friday afternoon.
Hundreds of people mourned the loss of the young lives as silence fell over the idyllic village.
Their devastated mother Kathleen, family and friends walked behind their two white coffins, with just the gentle sound of Twinkle Twinkle Little Star being sung as they made their final short journey from the family home to church.
Parish priest Father Declan Foley said the pair had achieved so much in their short few years and lived with such energy and intensity that they brought joy and happiness to their parents and local community.
The sudden and tragic death of the boys is beyond comprehension and almost impossible to put into words, but to remain silent would do Eoghan and Ruairi a disservice.
Father Declan Foley
Father Foley said it felt as if the earth had quaked and house had shook when their bodies were discovered on Monday in the boot of Chada's crashed car, four miles from Westport, Co Mayo.
It is believed they died of asphyxiation, which can be caused by strangling or suffocation.
Heartbroken school friends from Ballinkillen National School and teammates from Ballinkillen Hurling Club, Nurney Soccer Club and Fenagh Football Club formed a guard of honour.
About a dozen stewards from the locality lined the route and held up umbrellas to block the heartbreaking scene from the media.
They were buried together in a small cemetery in the church grounds.
Inside the church some of the boys' cousins and best friends carried a procession of symbols of their lives: a hurley, a football, toy tractor, cook book, golf club, bicycle and photograph.
Father Foley said photographs have portrayed the beautiful closeness and love between the brothers and manifests perfectly their relationship.
"Although the boys have their own rooms, they always slept together in the one bed," he added.
Eoghan and Ruairi's love of sport, cooking and farming were remembered throughout the emotional service, where school children and the church choir sang some of their favourite hymns and teachers and relatives read prayers of the faithful.
Prayers included the boy's favourite Bible story, Noah's Ark, and a reflection in Hindu by Father George Augustine, an Indian priest from Portlaoise.
Father Foley revealed the eldest brother loved experimenting in the kitchen and that his latest ambition was to be a chef, but kept his options open after he recently bought a calf with his communion money.
"Little Ruairi loved nothing more than helping Poppy, as granddad Billy is called, around the farm," he continued.
"He was going to be a tractor driver when he grew up.
"He was also looking forward to making his First Holy Communion and making some money.
"If Eoghan could buy a calf, he was going to buy a combine harvester," he added.