Their mother Puji Kuswati attacked worshippers at another church with her daughters aged 9 and 12.
An eight-year-old girl, who was reportedly with the family, survived the blast and was being treated in a hospital, said an East Java police spokesman. Bombings on three churches and a police headquarters are believed to be coordinated.
The new spate of bombings comes just ahead of the holy Islamic month of Ramadan, and follows a melee at a detention center near Jakarta last week in which jailed Muslim extremists killed six officers.
A second is the attackers, who appropriate the name of a worthy and long-established faith that espouses tolerance, justice and civil harmony, have about as much to do with Islam as the Klu Klux Klan has to do with Methodism, the Roman Catholic Church or Anglicanism.
Police in Sidoarjo, near Surabaya, recovered pipe bombs at an apartment where a blast on Sunday killed three members of a family alleged to have been making bombs.
Her brother Jo Prajoko told CNN he had dropped his sister and nephews at the church for Sunday prayers and was driving away when the bomb exploded.
According to Michelle, security has grown tighter since the incident, which has helped her feel at ease in the wake of terror. The father was shot by police as he held a detonator.
Yesterday, a counter-terrorism source told The Straits Times that a key reason why male militants are willing to sacrifice their wives and children in their "martyrdom" was because they did not want their surviving spouse and children being placed in deradilcalisation programmes after their death.
The use of children in the attacks has been particularly horrifying to people. The bombings, the deadliest in Indonesia in more than a decade, also wounded 40 people.
A security camera video of the attack on Surabaya's police headquarters showed at least one explosion after the four attackers rode two motorcycles up to a security checkpoint.
The clampdown was largely credited to the creation of a special anti-terror division called Densus 88, or D88. "They (were) competent, created good counterintelligence through (questioning) and developed the capacity to detect splinter cells and apprehend militants".
The flurry of bombings raised concerns that previously beaten-down militant networks in the world's most populous Muslim-majority nation have been reinvigorated by the return of some of the estimated 1,100 Indonesians who went to fight with the Islamic State group in Syria.