Sarah Barrass and Brandon Machin, who is her half-brother (brother by blood), strangled Tristan and Blake Barrass, aged 13 and 14, in Shiregreen, Sheffield, in May.
Barrass and Machin, 39, were both sentenced to a minimum of 35 years in prison at Sheffield Crown Court.
They have both previously admitted murder, conspiracy to murder all six of their children, including Blake and Tristan, and five counts of attempted murder.
The court heard how Barrass strangled Tristan with her dressing gown cord, before Machin strangled Blake with his hands. They then put plastic bags over the boys' heads, suffocating them.
South Yorkshire Police said Barrass, of Gregg House Road, Shiregreen, and Machin, of Burngreave Road, had been in a secret sexual relationship for years. Fearing they would be found out by the authorities and their children taken into care, they hatched a plot to kill them. Police said the plan was for Machin to discover what had happened and raise the alarm.
On the evening of 23 May, Barrass tried to poison the four eldest children, by collecting tablets prescribed to one of the children for ADHD and forcing them to swallow them. When it became apparent the plan had failed, Barrass began to search online for other ways of killing her children, including suffocation, strangulation and drowning.
She contacted Machin to tell him they were still alive and the pair then strangled the boys and placed bin bags over their heads "to ensure their certain death", Ms Melly said.
The defendants then ran a bath and repeatedly tried to drown one of the younger children. When that too failed, Barrass took the surviving children - two of whom are under the age of 13, and two under three - to the bedroom and phoned the police.
The court heard she told police she planned to kill the younger two children and herself, after the older four had died.