This is not a question! My purpose here is to keep this topic alive and to thank huntergrn for the answer. The answer (if you don't want to read my song and dance) is "avidemux2" and you can get it free using the link below to huntergrn's post here.  

My Song and Dance:  

I have been plagued from time to time with XYZ_Sc03a.avi and XYZ_Sc03b.avi which can't be joined because their audio sampling rates are different. I don't really know how that happens in the first place, but I do know it is a pain in the ass!  

Nandub will handle the VBR files ok and will split them and even append one to another as long as the audio sampling rates are the same. But, when you use Nandub to open XYZ_Sc03a.avi (a hypothetic file name) and then attempt to append part b, the message which appears is:  

"Cannot append segment: The audio streams have different sampling rates . . ."  

I have tried doing things like exporting the audio to WAV or other things people have been kind enough to suggest. But I've never been smart enough to make it work. The tool that has worked for me is "AviDeMux2" which is available at no charge under the GPL and you can find out about it here:  

http://www.hcmf.com/c/v4.cgi?4141-1  

When you open a video stream which has Variable Bit Rate audio, AviDeMux prompts you to make a time map of the audio. Say yes! Then, it will offer to unpack the bitstream. I pick "Yes" even though I don't know if that is required. Each of those operations should take less than 30 seconds and each will be repeated for the second segment. Then simply click on Save and the combined file will be saved using the location and name you choose.  

SOME TIPS:  

AviDeMux2 does not automatically save the new file in the same folder the sources were obtained (unlike both V-dub and Nandub). It defaults to the last place something was saved when the program was used.  

While it does take a minute or so to create the VBR time maps and to unpack the bitstreams, the saving of the resultant file is faster than either V-dub or Nandub.  

The program may have other cool features. One feature of great importance is that it is currently under development. V-dub is also under development, but V-dub doesn't mess with VBR audio at all --- just refuses to open the file. Nandub, a hack of V-dub which does allow VBR audio for direct stream copy, is no longer in development as far as I can tell.  

AviDeMux2 is available for various O/S:  

"Avidemux is available for Linux, BSD, Mac OS X and Microsoft Windows under the GNU GPL license." from the download page.  

Highly recommended!!  

Thanks, huntergrn.