Terrence O'Dowd is a wealthy man. At some point prior to 1898, he married a woman named Allison, who is much younger than him.
Events of Red Dead Online
In the mission "Love and Honor", his wife is supposedly kidnapped by a gang of outlaws, leaving Terrence very concerned about her. He visits the Sheriff's Office in Tumbleweed and pleads to Sheriff Freeman to mount a rescue, when the protagonist and their posse arrive. Citing the lack of manpower available to him and legal authority to do so, Freeman subsequently refers him to the present posse. Terrence then begs them and when they agree, he states his wife is being held at Twin Rocks.
Once there, however, the protagonists discover that Allison wasn't kidnapped, but rather ran away to be with her lover Cliff, and that she despises Terrence. The players are then give the choice of either helping Cliff and Allison escape, or killing Cliff and taking Allison back to her husband by force.
In the players choose to help, they take Allison and Cliff to their destination, while fending off gunmen hired by Terrence to try to rescue Allison.
If the players choose to kill Cliff, they do so, tie up Allison, and deliver her back to Terrence, who is glad to be reunited with her. He unties her and pays the protagonists before leaving with Allison, all the while she expresses her hatred towards her husband.
As shown in the few interactions with him, Terrence prefers women that are much younger than him, though he seems to genuinely love Allison and is concerned when she is apparently kidnapped. However, judging by Allison's hatred towards her husband, it can be assumed that Terrence doesn't treat her well, and regards her just as a trophy wife. In the scenario where Terrence is reunited with his wife, he appears to be happy to see her again and calls this the best day of his life. However, when Allison states how much she hates him, Terrence claims that his wife is deranged and that they just had a little misunderstanding.