Both sides say the other is responsible for the meeting not going ahead as planned.
Dunderdale has said she agreed to meet with Burton Winters's grandmother, Charlotte Winters Fost, to talk about the 14-year-old boy, who went missing while snowmobiling in coastal Labrador.
Search and rescue efforts for the boy have been criticized.
But Winters Fost says Dunderdale balked at the idea of a retired search and rescue co-ordinator sitting in on the meeting.
She says the Premier's Office told her that Kevin O'Brien, the provincial minister responsible for fire and emergency services, would replace Dunderdale.
The premier says that's when the family backed out of the meeting.
Dunderdale says she would be happy to speak with the family about Burton, but O'Brien is better able to answer questions on the search and rescue response.