I beat my dad four times in a row. Is an unrated game a good, sporting choice?

I think in this case, an unrated game, may be a good move, and I will help him avoid some blunders that can lead to losing his queen, or a fancy rook king fork, which he has trouble seeing in advance.  But, I think an unrated game can be good, while at the same time, I think letting your opponent win is never helpful for them increasing their skills.  So, with chess chat, I can help him avoid pitfalls, and then still structure my practice over reaching imbalanced exchanges, and work on my structure at the same time..?

Sure.  If you're playing numerous games with someone who you know is a weaker player than you, playing unrated games is the way to go.  It doesn't artificially inflate your rating and keep tearing theirs down.  Plus that way you can help offer advice and help him get better.