Sony Vegas will do it. Import video. Add additional stereo track. Insert new audio in said track. Line up audio. Remove old audio track. Render to a new DV-AVI file, then compress to whatever format or author to DVD (using something like Sony DVD Architect).
Edit:
And prepare by having PLENTY of HDD space. One DV tape is like 16GB of HDD space. I would plan to have at minimum triple that in free HDD space.
I don't use Vegas, so maybe this isn't as doable, but couldn't you just import the video, extract the audio into a .WAV file. Then in your favorite audio editor synch up the good audio with the original, and save the synched good audio. Encode the AVI file into streams, but then when authoring use the synched good audio instead of the original. No need for a second huge AVI file just to replace the audio that way, and it might be a little faster? I do this with WinDV to import, VirtualDub to extract the audio (well, first to trim the AVI file to exactly where I want if I don't get the capture quite spot on), CEPro to synch the audio, TMPGEnc to encode, DVDLabPro to author. Kind of a circuitous route, but it works well for me. And, I let the video encode on a second computer while I work on the audio synching, so that helps speed things up a bit.
My edit: sorry, not sure that quite fits the bill in the initial question for a single program answer (or simple, for that matter). But several of the tools are free and some of my other ones could be replaced by free- or shareware. The big issue, though, is getting something that can synch up the audio--any multitracking audio editor ought to be able to do that, so maybe you have the tool already, then just encode and author the DVD as you would if you weren't replacing the audio.