I have a typical web application, which is automated by Selenium WebDriver. My problem is a particular case of automation in which I have a link, which runs a swing app with
Since Java web start applications are basically regular Java applications and are not appearing in the DOM, you can't access them using WebDriver.
The best tool I know for testing AWT/Swing application is Jemmy. I usually use it for testing standalone Swing applications, but I am sure you can use it also for applications that are launched using the web start mechanism.