Ask this question again in the live/stage forum, they are the experts. What you propose with the three free-running DVD players can *sort of* work, in a rough sense, but they will never really be precise enough for matching action or dialog that has to span or move between the screens. For that, you would use either industrial dvd players with a special synchronized playback controller, or these days, most often, a computer (or several) and software to play synchronized files from a hard drive. Advising you on which of those to use is what the experts in the Live/Stage forum can help you with.
There is one other “cheat” method folks sometimes use. The Matrox brand triple-head adapter allows you to play one source out of a computer onto three screens as one very wide file, like a super-wide aftereffects composition. Obviously because its just one file, you never lose synchronization. That setup only needs the one file and one computer to play it out to three screens or projectors, so it is cheap and relatively simple, but it has limitations. Let the LS experts explain what they are.
Good luck with your project.