When you connect your iPod or iPhone to your computer, click on your device from the left pane and you'll see that iTunes offers some basic controls over personalization. You can choose exactly what photo libraries, music playlists, podcasts, videos, and contact data you want to automatically sync to your particular iPod, as well as what content you want to ignore.
Unfortunately, there's no iPod checkbox that will automatically detect which music in your iTunes library belongs to you, and which music belongs to someone else. You can add this function, however, in the following four steps.
Now, let's make a second playlist, this time a Smart playlist I'm calling "Donald's iPod," where the Playlist values exclude our "Don't list," as well as podcasts, and any music genres we know we don't like. You can add as many filters as you want by clicking the "+" symbol on the right side of each field.
If your iPod or iPhone can't hold much music, use the "Limit to" function underneath the filter list to generate a finite list of preferred songs that randomize each time you launch iTunes.
Both your playlists should appear in the column on your left. Check them out to make sure everything is working the way you want. If you find more bad music down the line, just add it to your "Don't List" and it will automatically be taken off your Smart playlist. If you discover a new genre that you want to filter out from your Smart list, just right-click the playlist, select edit, and make the necessary adjustments.
Finally, go back into your iPod's device window in iTunes (make sure your iPod is connected). Click on the music tab and set your iPod up to only sync music from the second playlist you created (the Smart playlist). Then, hit the "Apply" button in the lower right corner and celebrate your victory over your family's bad taste in music.