Character Analysis
A minor character calls this lady "Field Marshal Barbara"—and for good reason. When she opens her villa for an afternoon of pleasure (ahem, "collective sex entertainments"), she's pretty serious about it—and she doesn't take kindly to anybody who doesn't take pleasure seriously, either.
Barbara understands—as Kundera, Jan, and Petrarch do—that laughter is deadly to sexual pleasure. Once laughter is introduced, the farce is stripped bare: nobody would be able to take themselves seriously. It would leave her guests wallowing in the hilarity of the orgies they were participating in, and there's no way the field marshal will have any of that.
Barbara does indeed have major control issues. But she's not just managing the details of her personal life; she's orchestrating the sexuality of dozens of strangers. Jan observes that "we're all characters in Barbara's dream," and his new acquaintance (the bald man) notes that it's an impossible job: "But it never quite works. Barbara is like a clockmaker who has to keep moving the hands of his clock himself" (VII.13.11).
So Barbara really does have her work cut out for her, fighting against the hilarity that threatens the illusion of sensuality. While she seems to have enough people willing to play the game by her rules, Jan and the bald man unwittingly unbalance the delicate chemistry of Barbara's afternoon of pleasure. Their laughter unmasks the futility of Barbara's efforts—and earns them a one-way ticket to the sidewalk.