Welcome aboard to the fourm
To me, it seems rather unusual for the TV to affect the DVD recorder’s picture. It is like as if the DVD recorder is capturing the backfeed from the TV rather than from the satellite receiver directly.
There are two methods you can try hooking up the DVD recorder & Sky box:
Method 1: Connect the TV-Out of your Sky Digibox to your TV via SCART and connect the TV-Out of your DVD recorder to your TV via SCART. Finally, connect from the VCR Output of your Sky Digibox to the 2nd SCART socket of your DVD recorder.
Method 2: Connect the TV-Out on your Sky Digibox to the Auxilary input on your DVD recorder and connect the TV-out on your DVD recorder to your TV.
The First method would be my recommended way of hooking up a DVD recorder with a satellite receiver and this assumes your TV has two SCART inputs. The 2nd method should also work, which I would recommend for TV’s with only one SCART input, however there is a risk of capturing the on-screen display of your Sky box (if any is shown during the recording).
If you still have issues, it will be worth changing the TV output mode on your satellite receiver to ‘Composite’ instead of ‘RGB’ to see if this helps.