>The button drags but does not remove. I'm not at all sure that this isthe way to do this. Can someone point me in the right direction?

You need to remove the button from the grid, it's not a child of the StackPanel. The StackPanel is the target you want to add it to.

Grid Name="OuterGrid"

   private void panel_Drop(object sender, DragEventArgs e)
      {
      StackPanel parent = (StackPanel)sender;
      Button button = (Button)e.Data.GetData(typeof(Button));
      Point p = e.GetPosition((IInputElement)this);
      OuterGrid.Children.Remove(button);
      parent.Children.Add(button);
      }