What is the main conflict and it's resolution

The main conflict is between Davie and his Uncle Ebenezer. Davie is excited at the prospect of kinsmen, especially noble, kinsmen. Unfortunately, his Uncle is strange, and the great house is a shambles. His Uncle also spends an inordinate amount of time locking Davie in his room, and avoiding questions about family history.

The conflict is resolved when Davie is finally granted a meeting with Mr. Rankeillor (Ebenezer's lawyer). This meeting resolves the mysteries, and Davie finds that he does has a claim on his Uncle's property.