If you're talking about what I think you're talking about, then you should
be able to register the mouseListener to the parent and then move around
via the MouseEvent.getSource()

I'd give you the code to do that, except that I'm still unsure whether or
not this would be easier with the AWT Drag 'n Drop...

Sample compilable code:

I can drag the JLabel, but I can't drag the JButton, even when it is
disabled.

How do I get the mouse events to not be gobbled by the disabled
JButton?
OR How do I get the JButton to pass those mouse events to the parent
container?

import javax.swing.*;
import javax.swing.text.*;
import javax.swing.border.*;
import java.awt.*;
import java.awt.event.*;

public class DragSample extends JPanel
       implements MouseListener, MouseMotionListener {

   private JButton dragButton;
   private JLabel label;
   private JPanel parent;
   private JComponent dragging = null;
   private int mOffsetX, mOffsetY;
   private boolean disabled = false;

   public DragSample() {

       setLayout(new BoxLayout(this, BoxLayout.PAGE_AXIS));
       JToolBar toolBar = buildToolbar();
       add(toolBar);

       parent = new JPanel();
       add(parent);
       parent.setBackground( Color.white);
       parent.setPreferredSize(new Dimension(640, 480));
       parent.addMouseMotionListener(this);
       parent.addMouseListener(this);

       // Create a button.

       dragButton = new JButton("Drag Me");
       parent.add(dragButton);

       // Create JLabel
       Border myBorder = BorderFactory.createLineBorder( Color.red );
       label = new JLabel("Drag me");
       label.setBounds(0, 100, 50, 50);
       label.setBorder(myBorder);
       parent.add(label);

   }
   private JToolBar buildToolbar() {

       JToolBar toolBar = new JToolBar();
       toolBar.setRollover( true );
       toolBar.setFloatable( false );
       JButton disableButton = new JButton("Disable");
       disableButton.setToolTipText( "Disable 'Drag Me' Button" );
       disableButton.addActionListener( new ActionListener() {
           public void actionPerformed( ActionEvent e ) {
               disabled = true;
               dragButton.setEnabled(false);
           }
       });
       toolBar.add( disableButton );
       return toolBar;
   }

   /**
    * Create the GUI and show it.  For thread safety,
    * this method should be invoked from the
    * event-dispatching thread.
    */
   private static void createAndShowGUI() {
       //Make sure we have nice window decorations.
       JFrame.setDefaultLookAndFeelDecorated(true);

       //Create and set up the window.
       JFrame frame = new JFrame("DragSample");
       frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

       //Create and set up the content pane.
       JComponent newContentPane = new DragSample();
       newContentPane.setOpaque(true); //content panes must be opaque
       frame.setContentPane(newContentPane);

       //Display the window.
       frame.pack();
       frame.setVisible(true);
   }

   public static void main(String[] args) {
       //Schedule a job for the event-dispatching thread:
       //creating and showing this application's GUI.
       javax.swing.SwingUtilities.invokeLater(new Runnable() {
           public void run() {
               createAndShowGUI();
           }
       });
   }

   //
============================================================================
   // Mouse and Mouse motion event handlers

   public void mouseDragged(MouseEvent e) {
       if ( dragging!=null ) {

           int newY = e.getY() - mOffsetY;
           int newX = e.getX() - mOffsetX;
           dragging.setLocation(newX, newY);
       }
   }
   public void mouseMoved(MouseEvent e) {} //do nothing
   public void mouseExited(MouseEvent e) {} // do nothing
   public void mouseEntered(MouseEvent e) {} // do nothing
   public void mouseClicked(MouseEvent e) {} // do nothing

   public void mousePressed(MouseEvent e) {
       int cx = e.getX();
       int cy = e.getY();
       System.out.println("MousePressed event");
       // Find which component, if any, the mouse is over
       int lx, ty, rx, by;
       lx = label.getX();
       rx = lx + label.getWidth();
       if ((cx>=lx) && (cx<=rx)) {
           ty = label.getY();
           by = ty + label.getHeight();
           if ((cy>=ty) && (cy<=by)) {
               dragging = label;
           }
       }
       lx = dragButton.getX();
       rx = lx + dragButton.getWidth();
       if ((cx>=lx) && (cx<=rx)) {
           ty = dragButton.getY();
           by = ty + dragButton.getHeight();
           if ((cy>=ty) && (cy<=by)) {
               dragging = dragButton;
           }
       }

       if ( dragging != null ) {
           lx = dragging.getX();
           ty = dragging.getY();
           rx = lx + dragging.getWidth();
           by = ty + dragging.getHeight();
           if ((cx>=lx) && (cx<=rx) && (cy>=ty) && (cy<=by)) {
               mOffsetX = cx - lx; // offset from mouse pointer to loc
               mOffsetY = cy - ty; // of region
           }
       }
   }

   public void mouseReleased(MouseEvent e) {
       
       dragging = null;
   }

}