In the future, Swing related questions should be posted in the Swing forum.
Well, one thing you need to do is change the overall design to separate out the GUI from the parent container (JFrame or JApplet). Check out replies 27 and 30 of this posting for a simple way to do this.
http://forum.java.sun.com/thread.jspa?threadID=5145907&start=27&tstart=0
You may want to read the whole posting as it is a design related question, but I think the above two replies are specific to your question.