Get a smaller cage if needed for the coop, or if you feel the run is predator proof enough, you can leave them caged in the run instead.I have a 7 foot chickenwire "playpen" I use for the chicks to explore outside. The older hens free-range for about 2 hours each evening. I have a small wire cage that I put inside the run during the day, but I'm not sure how I would keep them apart at night unless I move the cage into the coop?
They really need to be around the hens most/all day for about 1-2 weeks of see but not touch, before I'd let them out to actually meet face to face. 1 hr a day isn't enough, you want the hens to see them, get used to them, and lose interest in them.