This two part series of missions are only available if you have a high Honor rating with Arthur. If you need help increasing it then consider finishing off the Loanshark missions for a huge boost. They’re short missions that tie up loose ends so it’s well worth playing through them twice, the second time skipping cutscenes for the Gold Medal.
Head to Annesburg to get started, you’ll find Edith Downes in the north side of town in a mess. As Arthur attempts to help her, she turns him down and notes that her son is working in the mines. Mount your horse and head up to the mines as quickly as possible to intervene in a dispute between Archie the foreman. You only need to knock down the Foreman in this brawl so ignore the other miner and focus on him, using counter attacks to knock him down as quickly as possible. In the cutscene that follows, Arthur will hand over $30 to Archie and the mission will complete.
Wait four in game hours after completing part I (camp outside) and return to Annesburg to begin the second part of this mission. You won’t need to skip the cutscenes this time as you’re only timed on the first part of the mission.
Once you learn that Edith is refusing to leave town and is currently on a job right now, Arthur takes off to find her. Mount your horse and head north up the tracks and then veer off to the left once you reach the marked area. Quickly activate your Eagle Eye to spot some marks and follow them to the northwest, taking a right when the path splits. You’ll find Edith and her customer here as Arthur scares him away before trying to encourage her to come back to town. Ask or Demand, either way the outcome is the same and she agrees to come back with you. Gallop back to Annesburg and meet up with Archie to complete this mission.