FinalCutPro3 and Deinterlacing

[Videogame4]

I've been making AMVs for a while now. Nothing really for serious competition. However, I want to really improve the quality of my videos now. The videos look fine when I've written them directly to either DVD or VHS with the program. However, when I try to convert the video either from the FCP file or from the DVD I wrote the video to using VirtualDub, suddenly I have some really bad interlacing problems.

So, my question is what I am doing wrong in FCP, if I'm missing a step, or if I just need to download a specific convertion program? It was never anything I really worried about as I just enjoy make these, but now I want to show what I can really do, ya know?