For some reason, in the first actual mission of the Auomatron DLC, when I defeat the robotrain, that I get the objective to search through his stuff, it doesn't update the mission objective like it does for everybody else. I've tried re-doing the mission multiple times in various ways, but it always ends up in the same problem. How am I supposed to pass the DLC storyline when it doesn't even let me pass this mission?

Have you tried reloading a save prior to going to the factory? Sometimes i get an audio glitch that i need to reload to a different save and back to fix