The "hard problem" as you probably know is actually a phrase referring to the problem of accounting for consciousness. Most things are not conscious. This table we are sitting at isn't conscious. Vegetables aren't conscious. We are conscious, and nobody understands how we do that; physically, scientifically or metaphysically. Nobody really knows; and that's the "hard problem."
Curiously, one of the reasons the play falls short of Pulitzer Prize-winning Margulies's usual vaunted mark is that he's chosen, as many playwrights before him have, to make The Country House an homage to Chekhov. To be more specific, he's saluting--if you want to call it that--The Seagull and Uncle Vanya, and he goes seriously awry doing so, falling far short of Chekhov's dramaturgically and emotionally involving level