I must confess I don't fully understand the situation you describe, particularly the phrase "separate desktop".
But if you've got it connected as described, the actual image being sent to the DVD recorder should be identical to that on your primary monitor.
However, it's important to appreciate that there will be a considerable difference in the image /resolution/ of the monitor display, and what the DVD recorder will record.
The resolution of the display on your primary monitor will be whatever you have set under Properties-Settings-Screen resolution, e.g. 1280x1024 pixels.
But the image resolution of the output from the SVID port is a fixed 768x576 pixels (for 'PAL'), so as to be compatible with the DVD recorder.
Does that assist? If not, could you clarify what you mean by "separate desktop" please?