Irish county of Carlow on Sunday evening.
The schoolboys were found dead on Monday in the boot of the family car, crashed by their father outside Westport in Mayo county.
According to local media reports, police are questioning Chada on suspicion that he murdered his children then tried to take his own life by crashing his car into a wall.
The father, who has been described by his neighbours as a "prefect devoted dad", is believed to have strangled the kids.
The 'Irish Independent' has reported that Chada, known locally as 'Sanj', is linked to a 50,000 Euro embezzlement case in Carlow and an investigation is about to begin.
A priest comforting the boys' mother, Kathleen Chada, said: "It was like an earthquake had hit the house. It was devastating for all of us. You can't put into words the shock and numbness and pain and grief of that news coming through." Officers in Mayo have confirmed that Chada is in an "extremely distressed" state but he will be arrested on suspicion of murder when doctors say he is fit enough to be discharged.
He had to be cut from the wreckage of his car by a fire crew and witnesses described how the car careered down a by-road at speed before crashing into a wall.
Reports say he was found in the car with a makeshift noose around his neck and was taken from the scene of the accident to Mayo General Hospital for treatment to his injuries.
He had left his home with the two boys on Sunday night to take them bowling as a treat.
When they failed to return home, the worried mother raised an alarm and police launched a nationwide alert.
Gardai, as the Irish police is known, issued the first-ever amber alert for missing children - the Child Rescue Ireland Alert - after Chada failed to return home with them.
At the time the alert was issued, Gardai said they had no knowledge of any breakdown in relations in the family and insisted that the couple were not estranged.
Eoghan and Ruairi were described as extremely popular and "two little sports fanatics".
They were members of their local junior hurling club, Ballinkillen in rural Carlow, and had played at under-10 and under-six level.
Mrs Chada, a nurse, was originally from the area and lives near where her parents have a home.