Kersh,
Is the trigger for the bottom barrel (I'm guessing the rifle barrel in the combo set) a single set trigger? If so, it will have a small screw behind it. If it is a set trigger, push it forward until it "clicks" and it will have a very light "pull". You can live with 12-pound shotgun triggers, but not for a rifle. before you do anything permanent you might super glue a thin shim into the sear notches and see how you like that.
Mike