@FatFire: Just gonna try to repeat what you said to make sure I understand what you have: a swing application, with lots of objects to be rendered, on an old graphics card? And that the rendering takes so long, that it takes processing time away from having the GUI react in real-time?
If I’ve misunderstood you, then ignore the rest of this post
If you’re on a single-core CPU, then I think the problem here isn’t really about trying to multi-thread the program, but rather that you don’t have enough processing power to do everything you want. You could try to reduce how much CPU time the Animator takes, by using the FPSAnimator instead, and setting a ‘good enough’ (low) framerate. (I think) The FPSAnimator only takes as much time as it needs to reach the desired framerate, leaving the CPU free when it’s not rendering.
This should free-up CPU time to help with the responsiveness of your Swing GUI.
If you have lots of complicated objects to render, you might want to think about optimizing the rendering of those objects. If you’re using OpenGL ‘immediate mode’ to render your objects (that is, when your rendering code has lots of glBegin() glEnd() functions), you might want to read about OpenGL display lists and vertex arrays to speed-up rendering times. Immediate mode is SLOW.
Putting ‘OpenGL performance optimize’ into Google gave me a few hits on pages which might help.