Question

Can the control drag the parent TimeItem to a different row and have all its associated sub items move with it?

Answer

There is no property to set to do this automatically; you will need to react to an event and move child time items according to your rules.

In GTP.NET I would suggest to implement OnTimeItem_ChangeRow and in this event track down the child nodes by e.TimeItem.GanttRow.GridNode.SubNodes[0..x] and for each SubNode y do Gantt.GanttRowFromGridNode(y) then loop over the layers and timeItems and move them the way you need (or move the whole GridNode to a new parent if that is what you want).