Samantha Ford was arrested last Thursday after two children, both aged 23 months, were found at a house in Castle Drive, Margate, in the early hours of the morning, Kent Police said.
The 37-year-old was due to appear at Maidstone Crown Court via video link on Monday charged with murdering Jake and Chloe Ford on December 26.
She had been available earlier in the morning but had "gone back to health care" by the time of the hearing, Ronnie Manek, for the defence, said.
David Griffith-Jones QC, honorary recorder of Maidstone, agreed that proceedings should continue in her absence.
Ford was remanded to appear at Maidstone Crown Court on January 31.
Any trial is estimated to last around three weeks and a provisional date has been set for June 24.
By Jemma Crew, Press Association