The father of Carla, Darragh and Conor McGinley says the family will be "forever heartbroken" following their deaths.
During the service, members of Rathcoole Boys Football Club - which Conor and Darragh were involved in - and Scoil Chronain, where they attended, hugged, cried and remembered the lives of what Andrew McGinley called his "wonderful children".
43 year old Deirdre Morley of Parsons Court, Newcastle is charged with the murder of her three children.
Detective Sgt Dara Kenny of Clondalkin Garda Station told the court Ms. Morley made no reply when the charges of murder were put to her at 2.49 this afternoon.
Judge Paula Murphy made an order affording her ongoing medical treatment in custody, and continuing psychiatric assessment and treatment.
Legal aid was also granted and the judge remanded Deirdre Morley in custody to appear again before Dublin District Court next Wednesday.