For a three-act plot analysis, put on your screenwriter’s hat. Moviemakers know the formula well: at the end of Act One, the main character is drawn in completely to a conflict. During Act Two, she is farthest away from her goals. At the end of Act Three, the story is resolved.
Act I
If The Ambassadors were your typical stage drama, Act I would be bookended by Strether's arrival in Europe and the arrival of Sarah Pocock. In this act, we first learn all about Strether's situation with Mrs. Newsome, including his engagement to her and his financial dependence on her. Also his mission to go to Paris and bring Chad home. But somewhere along the way, Strether finds that he actually loves being in Paris and even really likes Chad now that the kid has escaped the influence of his mother.
This just leads Strether to wonder whether he's wasted his own life trying to make other people (like Mrs. Newsome) happy. As time passes, Strether writes letters back home to delay things so he can enjoy Paris some more. But when he eventually makes the mistake of complimenting Chad and his companion Madame de Vionnet in a letter, Mrs. Newsome takes swift action to send her daughter Sarah to Paris to check things out.
Act II
Now that we know the stakes of what's happening in Paris, we bite our nails in anticipation as Mrs. Newsome's new "ambassador," Sarah Pocock, arrives in Paris. Strether and Chad take Sarah around to all the swanky parties and introduce her to Madame de Vionnet. And you can imagine she's not as happy about that as they are.
Strether's hopes that Sarah would be swept away by how wonderful everything is in the same way he was pretty much end up dashed against the rocks. The beauty of Chad's life in Paris just makes Sarah really angry, because she's offended by the idea that anything in the world is better than the Newsome family's life back in Woollett, Massachusetts. Come on, Sarah, live a little.
When Strether finally accuses her of being stubborn and prejudiced, she gives him the ultimatum of coming home immediately or not at all. Strether refuses and Sarah leaves, effectively ending Strether's engagement to Mrs. Newsome.
Act III
Now that Sarah is gone and Mrs. Newsome is no longer in the picture, Strether feels like he can stretch out and really enjoy Paris guilt-free. But the situation doesn't last long, because one day while walking through the French countryside, Strether catches Chad and Madame de Vionnet sneaking off to a countryside hotel. He realizes that their relationship is sexual in nature, and feels that he's been lied to the entire book. He was led to support Chad's life in Paris based on false assumptions about Chad's friendship with Madame.
Strether feels that he can't handle feeling left out anymore, and he decides to return to Woollett, Massachusetts. He won't necessarily return to Mrs. Newsome, but he can't stay in Paris feeling like a loser. Before he leaves, his lady friend Maria Gostrey, who's been flirting and gossiping with him throughout the book, begs him to stay so that they can be together. But Strether, seeing her as part of how he's been fooled, refuses.