The JMapPane class is primiarly used as a teaching aid for the tutorials used to explore the GeoTools library.
It is developed in collaboration with the user list, and while not a intended as a GIS application it is a good starting point for trying out your ideas.
There is a flying saucers demo you can review; but the real answer is to set up a second raster to draw your moving car into; and draw that over top of the map rendered by gt-renderer.
Remember that JMapPane is just a demo showing how you can use StreamingRenderer to draw into a BufferedImage. You can do the same thing in your own code; and have one buffered image for the map and a second one for your “overlays” including the moving car.
This really comes down to how you use the GeoTools renderer. Remember that the GeoTools renderer is doing a lot of calculation and data access; not what you want in the middle of animation.
The gt-renderer is optimised for memory use; it does not loading your data into memory (it is drawing from disk, or database, each time). You can experiment with loading your data into memory (specifically into a spatial index) if you want faster performance out of it.
For raster rendering you have a great deal of control over performance using JAI TileCache settings in addition to convering your rasters into an efficient format (anything is better than jpeg).