I would first demux the video and audio streams.
If you can load the MPEG-2 video as a source into your editing software directly, then great. Otherwise, you should first save it out to an AVI file using lossless compression. You will need a fair bit of hard drive space.
To edit the 5.1 audio, you will need to decode the AC3 file into six mono WAV files.
Never used Vegas but I think it is able to work with multi-channel audio. Certainly the latest version of Sound Forge can.