Sarah Barrass, 34, is accused of murdering Blake Barrass, 14, and 13-year-old Tristan Barrass following an incident in the Shiregreen area of Sheffield on Friday.
She appeared in the dock at Sheffield Magistrates' Court alongside Brandon Machin, 37, who is also accused of murdering the two boys.
The pair appeared on Monday morning, wearing grey prison t-shirts and flanked by three security dock officers.
Barrass began sobbing as soon as she entered the dock.
They spoke to confirm their names, dates of birth, addresses and nationalities during the 10-minute hearing.
The court heard that Barrass and Machin are charged with murdering the two boys on May 24.
Barrass is also charged with three counts of attempted murder against two other children.
No application for bail was made and they were remanded in custody to appear at Sheffield Crown Court on Tuesday.
Barrass could be heard shouting as she left the dock.
Police were called to a semi-detached house in Shiregreen at around 7.30am on Friday.
Detectives have given no indication about the nature of the incident, but have confirmed it was not a shooting, and said it was confined to one property.
A spokesman said detectives are not looking for anyone else in connection with the incident.