The incident was the latest in a series of attacks that coincide with efforts to hold peace talks between Thailand's government and Muslim separatist insurgents who have wreaked havoc across the country's southernmost provinces since 2004, at a cost of more than 6,000 lives.
Other recent attacks have included bombings across seven provinces popular with tourists that killed four people, and an explosive detonated on a rail line that derailed a train car and killed a railway worker.
The targets were traffic policemen and people dropping off their children at the Baan Ta Baa School, Noppadon said.
In addition to the father and daughter who died of their injuries while being taken to a hospital, a 23-year-old man who was one of eight people hospitalized died of his injuries.
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Thailand is overwhelmingly Buddhist, but its three southernmost provinces have Muslim majorities who have long complained they face discrimination.
A statement from UNICEF, the United Nations' children's advocacy organisation, said it was "shocked and saddened" by the incident.
The group Save the Children urged greater protection for children and educational institutions.