This topic should really be in the "General VLC media player discussion" (or "VLC media player for Windows" if you are running Windows).
However, how are you playing the DVD-Video in VLC? If you go to "File >> Open Disc...", try both the "DVD (menus)" and "DVD" options. Since it is a home-made DVD-Video it is unlikely to have copy-protection, so you could try going to "File >> Open Directory..." and selecting the "VIDEO_TS" folder insider the DVD also.
Does anyone know how I can copy the DVD onto my computer and then re-record it on a DVD+R?
As joseph5 said, DVD Decryter in File mode ("Mode >> File") should make a exact copy of the Files on the DVD-Video. You could then use e.g. InfraRecorder to record it to a new DVD.
Alternatively, DVD Shrink can copy the contents of a DVD-Video and save it as an *.iso (image file) file, which could then be written to a disc using e.g. InfraRecorder, ImgBurn or DVD Decrypter.
Cheers, Arite.