Explaining it doesn't take away the embarrassment they might feel, and the son probably won't just say "oh, there was a reason for it, so that's okay." And who says no one else cares? We know nothing about the size of their family, or their community of friends, then there's the professional community on both sides... I don't know about you, but if I was in Hutch's position as we left the end of Chapter 1, I wouldn't want anyone finding out what my wife was doing with my boss, and how I handled it (or didn't). And it's harder for me to put myself in Vivian's shoes, but I would suggest the exact same thing, she wouldn't want anyone to find out about it and start labelling her a whore, or whatever, or for other men to start coming up to her and propositioning her, since she's already dropping her knickers for someone else outside of the marriage...
It's not all about what other people think, as well. It's about what Hutch and Vivian think and specifically, how they think others will look at them, etc.
But, I'd say it's also one of those irrelevant ones, as I don't think it's going to come up in the game.