Dominic West portrays Richard Burton, who has recently quit drinking, and is persuaded by Helena Bonham Carter’s character, Elizabeth Taylor—who struggles with substance abuse—to come back together for a production of Noêl Coward's "Private Lives." He’s hesitant because he has other commitments, including a potential role as “Lear” and an upcoming marriage, but she manages to convince him. The show nearly doesn't hap…