Juliana Prosper, 48, was discovered alongside her son Kyle Prosper, 16, and daughter Giselle Prosper, 13, at home in Luton in September.
He is also accused of possession of a shotgun on September 13, as well as possession of a bladed article, a kitchen knife, in a public place on the same date.
"Giselle was a beautiful soul and caring young girl; she liked to laugh lots and loved her family and big brothers.
Nicholas Prosper, 18, appeared at Luton Crown Court today where he admitted three counts of murder.
Officers discovered Juliana and two of her four children dead inside the flat.
