When the play opens, we quickly learn that the children of Andrew Undershaft and Lady Britomart have been kept in the dark about some key matters. For example, Stephen, the only son, was apparently unaware that his father's plan to disinherit him from the family business was the reason his parents separated all those years ago. Surprise!
Also, on a more basic level, the kids haven't seen Andrew for a long time—and they don't know he's on his way over until right before it happens. Then, when Undershaft arrives, hilarity ensues as he tries to figure out which of the people present are actually his children—he mistakes his future sons-in-law for Stephen at first. So, yeah, there's a lot of confusion.
Undershaft is eager to defend himself against his wife and children's negative perceptions of his profession, challenging their views of morality/immorality and belief that the Undershaft factory does more evil than good. After bantering quite a bit with Barbara, whose enthusiasm for the Salvation Army makes her particularly hostile towards her father's profession, they each agree to visit the other's place of work and get some more clarity . . .
When Andrew visits Barbara at work, he ends up matching a massive donation to the Army made by a local whiskey distiller, which saves the organization from financial ruin. Most of the Army's employees rejoice, but Barbara is unhappy—in her view, it's wrong and hypocritical that the Army is now in the pocket of companies that make arms and whiskey. Barbara is pretty disillusioned by the revelation that everyone has a price . . .
Things take a sunnier turn, however, when Barbara and the rest of her family go to visit the Undershaft factory. The whole family is pretty impressed with the workers, the town, and the factory itself. Barbara's fiancé, Dolly, banters and bonds with his future father-in-law throughout the play and ends up agreeing to take over the family business. He's afraid that Barbara will be upset, but she's actually come around to the view that she can still be part of the Army and work to save souls without rejecting the family trade. In fact, because the factory will give her the opportunity to save some non-desperate folks, she apparently has come to believe her dad's business is doing a good thing for the world. And with that 180, the play closes.