BAGHDAD—An Iraqi family that lost two children in the boat tragedy that also claimed the life of 3-year-old Syrian boy Aylan Kurdi challenged an earlier version of how the vessel capsized, in an incident that has come to symbolize the migrant crisis.

Iraqi siblings Zainab Hadi, 11 years old, and Haidar Hadi, 10, drowned in their life vests when the 15-foot boat flipped over them last week, said their mother, Zainab Abbas. Ms. Abbas’s husband, Ahmad Hadi, the children’s father, arrived in Baghdad on Wednesday carrying the bodies...