To use your Cinema Display independantly, you will need to play the DVD from the computer attached to the monitor and not from your MBP. With the Apple TV, I think your MBP would still be doing the heavy lifting of playing the DVD and then streaming it across to the Apple TV.
I have already connected my MBP to my 55" using DVI to HDMI. DVI to DVI would be no different. Once connected, and have the screens set up, start DVD Player and just drag it to the cinema display. This leaves your laptop monitor free for whatever you want to do. Of course, if you are trying to play a 3d intense game while watching a DVD and both screens set to optimum resolution, this will push the video card to the extreme and may not respond so well. Using the Apple TV in this scenario would probably alleviate some of this issue, as you wouldn't be using the video card to drive both displays, but you would have the MBP playing the DVD and streaming it to the Apple TV.
If your issue is one of distance between your MBP and the cinema display, check out extending your DVI cables. This may be more cost effective if you can handle the cables lying around. The following link has some info on DVI cables and the possibilties.
http://www.scala.com/hardware/dvi-vga-cable.html
edit: at this time, don't think anyone really knows if you could stream a DVD playing or will it only work with video in iTunes.