Carol King is the widow of Stein, and mother to Carter, Clinton, and Kennedy. She had a sailor's mouth in her day, but does her best to be the mom character she thinks she's supposed to be. After her husband passes, she creates a twin version of herself, "Aunt Sylvia," in an attempt to make the kids feel like they still have plenty of family. It's ridiculous, but she keeps running with it in the hopes that it makes even the slightest difference.
Of note: the actor playing Carol has NEVER been the oldest actor. Indeed, at least one of her sons has been older than her in each of the 9 productions thus far. This play has no use for such standards. Whether it's having three sons, each of different racial backgrounds, or having said sons not all be "sons," or having a mother who is younger than some or all of her sons--or even not being "mother" in some traditional sense--it can work. And has worked.