Like The Apple Family Plays and The Gabriels, Richard Nelson’s new play, The Michaels, focuses on a family in Rhinebeck, N.Y., a destination that has become for this playwright what Idaho is for the dramatist Samuel D. Hunter. In Rhinebeck, Nelson finds a microcosm of American life, although his primary structural models are clearly the plays of Anton Chekhov. Nelson has had a hand in translating three plays by the Russian master, and Chekhov’s influence is evident in the quotidian concerns of the earlier families as well as this one: it’s the first in a third cycle.