Create a slideshow in iDVD with the "+" button at the bottom
and place the video cliips in it. Set the slideshow volume to zero.
That will let you play the movie clips without sound regardless of what the volume on the DVD player is set to. It essentially removes the audio from the video recordings.
Do not set iDVD to Scale Photos to TV safe area in iDVD's Slideshow preference pane.
If you put more than one video clip in a slideshow do not use any transition.
If you want the multiple clips to play one after another in an iDVD slideshow select any slide duration except manual.
Also I suggest you follow this workflow in the creation of your iDVD project and disk:
Once you have the project as you want it save it as a disk image via the File ➙ Save as Disk Image menu option. This will separate the encoding process from the burn process.
To check the encoding mount the disk image and launch DVD Player and play it. If it plays OK with DVD Player the encoding was good.
Then burn to disk with Disk Utility or Toast at the slowest speed available (2x-4x) to assure the best burn quality. Always use top quality media: Verbatim, Maxell or Taiyo Yuden DVD-R are the most recommended in these forums.
If I remember correctly, doing as Old Toad suggests will also not play any sound within the video itself.
To remove the background music only.
Click on 'Show the DVD Map' (three squares liked together) as seen below Slideshow Volume in Old Toad's picture.
Double-click right square.
Select MP3 (left of Slideshow Volume) and drag outside to delete it.
Use Return to get back.
Video sound - On. Background music - Off.