After much toil I got my click thing working fine.  Sadly, When I change the format of my JTextPane to "text/html" and add text to the JTextPane my button disappears. I am almost done with this harsh mistress. Could anyone help?
Code follows...
import java.awt.*;
import javax.swing.*;
import java.awt.Color;
import javax.swing.JTextPane;
import javax.swing.JButton;
import java.applet.*;
import java.awt.event.MouseAdapter; 
import java.awt.event.MouseEvent; 
public class jlabeltest extends Applet {
    public void init() {
        jlabeltest textPaneExample = new jlabeltest();
        textPaneExample.setSize(550, 300);
        textPaneExample.setVisible(true);
    }
    public jlabeltest() {
        JTextPane textPane = new JTextPane();
        textPane.setContentType("text/html");
        InlineB button = new InlineB("Button");     
        textPane.setText("<p color='#FF0000'>Cool!</p>");
        button.setAlignmentY(0.85f); 
        button.addMouseListener(new MouseAdapter()  {   
        public void mouseReleased(MouseEvent e) {
        if (e.isPopupTrigger()) {   
            JOptionPane.showMessageDialog(null,"Hello!");
            // Right Click   
        }   
        if (SwingUtilities.isLeftMouseButton(e)) {
            JOptionPane.showMessageDialog(null,"Click!");
            // Left Click
        }
    }   
    });  
        textPane.insertComponent(button); 
        this.add(textPane); 
    }
}