If your recorder is producing .VOB files then PRE can struggle (too many DVD devices do *not* conform to the DVD standards) and you should probably convert before import. Is your recorder a hard disk unit as well? If so check to see if it has any other export formats.
Whatever though, the ADVC unit should work just fine (you'll also need to connect an audio output from your recorder as well).
Insanity is hereditary, you get it from your children
I use a similar A-D bridge and just play from my DVD player through it to PrPro (in my case), and it works fine. Obviously, you do not have Device Control, as the DVD deck is not hooked up with cables that will control it. However, with the player's remote in one hand, and the mouse in the other, I just start the Record, then the deck, and Trim off those first few, blank frames.
As Neale points out, most DVR units create DVD's that are not 100% DVD-compliant, and this creates a problem for PrE (and PrPro). Also, since you are having issues with the Audio, my guess would be that the DVR is producing AC3 (one of the two possible standards for the primary Audio stream,) but that it is not 100% Dolby Digital standard. Many DVD producing machines, and a lot of authoring software, play very fast and loose with the DVD-specs., and this is what causes exacting programs, like PrE, to fail to work with the VOB's correctly.
If you are still having issues with Audio, here are two workarounds:
1.) use the excellent, free audio-editing program, Audacity, to rip the Audio from the DVD. This should work fine with the DVD in the computer's DVD drive. Once ripped, just do a Save_As PCM/WAV 48KHz 16-bit.
2.) instead of doing the Capture in PrE, use a program, like SceneAlyzer, to do the Capture via the Canopus unit.