The tragic incident took place around 11am at the Upazila’s Bhaorkhola village, police said.
The deceased are Rekha Aktar, 27, wife of Alamgir Hossain, couple’s daughter ‘Sumaiya’, 8, and son ‘Emon’, 5.
Local Union Parishad Member Saab Miah said the family had been living hand-to-mouth for a long time. They had a row on Tuesday night over their perennial financial hardship.
He said Rekha, who was emotionally unstable, first poisoned the children on Wednesday morning and then she herself took the poison.
Meghna Police Station OC AKM Mohsin Khan also confirmed a long-time marital discord.
The mother committed suicide after poisoning the children, he added.
Police detained the husband, Alamgir, over the incident.
The bodies were recovered and sent to Comilla Medical College and Hospital for autopsy.