Theresa Riggi, 49, originally from California, is serving 16 years for the crime, which shocked the country in 2010.
She stabbed each of her children - Austin and Gianluca, both eight, and Cecilia, five - eight times at their second-floor Edinburgh flat.
She admitted culpable homicide on the grounds of diminished responsibility.
She was held in Cornton Vale Prison, Stirling, before being transferred to secure psychiatric care.
It is alleged that in November 2011 in Cornton Vale she was disfigured for life by another woman who was an inmate at the time, Angela Hamilton.
At Stirling Sheriff Court yesterday Hamilton, 40, from Glasgow, maintained her plea of not guilty.
She faces a single charge which alleges she repeatedly struck Riggi's face and head with the blade.
She faces trial in March.