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
Davie leaves his hometown of Essendean to seek out financial help at the Shaws household now that he has been left an orphan. He arrives at the house only to find that his uncle is a miserable miser who clearly wants Davie either to die or to disappear without troubling him anymore. Why does Ebenezer want Davie gone so bad? Because Davie seems to present some kind of threat to Ebenezer's property.
Act II
The second act is the part of the story where everything seems as far as possible from a conclusion. This moment comes pretty early in Kidnapped and is so dire that it takes around two hundred pages to bring Davie plausibly back from the brink of destruction. The second act starts in Chapter 7, when Ebenezer tricks Davie into getting on the ship the Covenant, sailing for the Americas. Davie's set to be sold into slavery once the Covenant reaches the Carolinas. He's kept heavily guarded and has no chance of escaping…until, that is, the Covenant runs into another boat with a certain Alan Breck Stewart aboard. Everything that follows – the bad times on Earraid, the Colin Roy murder, and their race across the Highlands – all fill the time between Davie's kidnapping and his return to Queensferry to reclaim his estate.
Act III
This is the moment when everything gets resolved: in other words, Chapter 28. Here, Davie meets with his lawyer back in Queensferry, who confirms that Davie does have a claim on Ebenezer's estate. Both Davie and Alan have safely made it from the Highlands (with all those Campbells and British looking for them) into the Lowlands, and Davie is pretty much home free. All there is left to do is to retrieve Davie's estate from Ebenezer and set Alan on a course to France.