Here's your process:
Video stored digitally on the DVR.
DVR outputs analogue composite video.
Camera converts analogue video to DV format.
DV is edited.
Edited DV then encoded to MPEG-2 for DVD.
It would be much better to get a direct digital copy of the data directly off the DVR, and I believe this is what Zeromancer was referring to when he mentioned a USB connection. This may not be possible due to encryption, DRM, etc...
You should check the DV AVI files are OK, but I would be surprised if they are out of sync; my guess is that the sync error is introduced during the editing. You could try skipping the stage where you trim your AVI files, to see if a DVD encoded from the unedited AVIs is still in sync.