A police officer said villagers rescued all the four members of the family and admitted them to Swahid Mukunda Kakati Civil hospital in critical condition.
The husband of the woman was not at home when the incident took place, the officer said.
He narrated the turn of events as the woman and her brother-in-law first feeding the two children with poison-laced food and then themselves eating the same food.
Neighbours further informed the poverty-stricken family was facing acute financial problem.