In case you have your purchased but copy protected DVDs, try DVDFab website, specifically the DVD Copy. The Windows version, which was named the DVD Decrypter, was a free program some years ago and it copied the entire DVD to a VIDEO_TS folder in a hard drive. Unfortunately the free version disappeared and these days it cost $49.
Anyway it basically copies the entire DVD to a VIDEO_TS folder, preserving the VOB file structure and more importantly the entire menu structure which allows you to access the entire DVD with its special features etc.
In your case, however, since you have your home made DVDs, you already have the VIDEO_TS folder handy. Just copy the entire folder to the hard drive.
Then, if you place the VIDEO_TS folder in a folder and make its extension .dvdmedia then Mac's DVD Player will open it as a regular DVD and you will have a full access to all the DVD Menus. Alternatively, you can also use the VLC Player for playback and have access to DVD Menus.
Handbrake does not preserve the original DVD Menus.