Black vacationers on Martha’s Vineyard often describe visiting the island in August as a kind of family reunion. If your family happens to include Michelle Obama, that is. “This is a special place for us, because, as you all know, this is where we come to enjoy being us,” Ms. Obama said Saturday afternoon at the Martha’s Vineyard African American Film Festival, where she joined her older brother, Craig Robinson, for a live recording of their podcast, “IMO,” which she likened to a kitchen table. The brother-sister duo were speaking with the actress Natasha Rothwell, whom they repeatedly referred to...