My guess (from only a quick look at the code, so I could be wrong) is that you're flooding the Sketcher with paint events. If the Swing event queue gets too full, responsiveness will go down until you stop moving the mouse and let it clear the events out.
Swing is supposedly able to combine repaints that happen before the paint method is actually called, but in your case you're repainting the Sketcher on every mouse move (from within the Swing event dispatch thread), and also on every timer tick (from a separate timer thread). Repainting the Sketcher on mousemove should be all that's required.
For the sibling repainting issue, you might look at isOptimizedDrawingEnabled at
http://java.sun.com/products/jfc/tsc/articles/painting/. Normally siblings shouldn't cause repaints on each other unless they overlap, but if a sibling is doing something weird like calling repaint on its parent, you could see this behavior.