[Low Key]

Perhaps a good way to get into the families.. good graces. Go, meet them, and ask to hear stories about ol' gramps. Maybe he was a really cool guy. Maybe you can learn something about his life that you can apply to your own short existence on this planet.

Or you could waste the day playing video games/golf/poker while severly destroying your current relationship.

All else aside, this seems like the perfect time to meet the family. Being there by itself shows that you care for their daughter, it shows you're a stand up individual. And most importantly, you don't really have to make much small talk. A simple "Hello, sorry for you loss" and you're off the hook. You'll never get another chance like this again. (And if the people really want a distraction, they can just ask this new person about himself, and any mundane BS he spouts off will help distract them, which they'll be grateful for. Ego boosting for you, a distraction for them, everyone's a winner!)