I totally missed that, on my first read. Yes, definitely be sure the DVD is already on the computer hard drive. If it's a commercial DVD that's being backed up for whatever reason, then it may need to be ripped with a tool like
DVD Decrypter, or DVDFab 6 (in free rip mode).
Have you considered avoiding the messy split scenario entirely, and simply using a Verbatim DVD+R DL disc to make your copy?