Sarah Barrass, aged 34, is charged with murdering Blake Barrass, 14, and Tristan Barrass, 13, who died after an incident at their Shiregreen home on May 24.
Emergency services were called and the children were taken to hospital but died a short time later.
Barrass, formerly of Gregg House Road, Shiregreen, is also charged with three counts of attempted murder against two other children, who cannot be named for legal reasons.
Her co-accused, Brandon Machin, 37, is charged with two counts of murder.
Both have been remanded in custody since their arrests and are due at Sheffield Crown Court on September 9.