The horizontal lines you're seeing during motion is most likely the effect of watching interlaced video on a progressive scan monitor. If when viewed on a normal CRT TV you do not see the lines, that verifies interlacing as the cause. If your intended audience is going to be viewing your DVD on TV, you can leave it interlaced. But if it's intended for viewing on computer or other progressive scan monitors, you can deinterlace the Sequence prior to exporting.
If you're end goal is making a DVD-Video, export your fully rendered Sequence from FCP "Using Compressor" and choose the appropriate preset for your program's duration. You can adjust the encoding parameters of any preset and save it for future use.
You can also export a reference or self-contained movie (do NOT re-compress all frames!) of your FCP Sequence and use that in Compressor or import it into DVD-SP and let it do the encoding.
-DH