for each of the child lists, you need to add a Set Selected In List and Populate List from array behavior to the onLoad event of the body tag.
the body tag onLoad event should have these dynamic Dropdowns behaviors applied in this order:
Set Selected in List - Set the selected item for the main parent list
Populate List From Array - Populate the first child list from the array
Set Selected in List - Set the Selected item in the first child list
Populate List From Array - Populate the second child list
Set Selected ion list - Set the selected item in the second child list