The children's father lodged FIR against her, they said.
Rekha beat Pooja (8) and Saurabh (6) to death, after which she consumed poison, SP (City) Srikant Yadav said.
The woman, who is the second wife of a class 4 employee, was rushed to hospital in serious condition, the SP said.
Domestic controversy is believed to be the reason behind the incident, Yadav said.