The older hens chase and peck the little girls and ( sometimes ) the rooster, other than that they get alone OK. Right now the younger ones are roosting garage and the hens sleep in the coop.
This is a typical issue when you merge immature chickens with mature chickens. Until they mature enough to force their way into the pecking order, the mature hens can be pretty brutal to the immature ones. If you have enough room during the day that's usually not a big issue, the younger ones avoid the older ones. But at night the hens can be downright nasty to the immature ones. I've seen a hen walk from one end of the roost to the other to peck a younger bird that dared try to sleep on the main roosts. So the younger ones look for a safer place to sleep.
Usually my pullets force their way into the pecking order around the time they start to lay. It can be a few days before they start of a few weeks after, but in that general time frame. Who knows with cockerels?M I've had a cockerel force his way in before 5 months, I had one that took almost 11 months. It depends on how fast he matures plus the attitude of the older hens. The older hens have a part to play in this too, it's not just the cockerel.
I ran into this a lot as I integrate younger chicks all the time. I've had a few sleep in a different building like yours but most of the time they just moved to the nests. You don't want them sleeping in the nests. So I put in a juvenile roost, about a foot lower than the main roosts, separated horizontally by about three feet (far enough the hens couldn't peck them), and higher than the nests to give them a safe place to go that is not my nests. I can't tell from your photo how you would manage to put in another roost lower than the main roosts and still be higher than the nests.
I imagine it is a pain having them sleep in the garage. If you wait until they mature enough they should move into the main coop on their own. Since they are 20 weeks old that may not be that long for the pullets and the cockerel will probably follow them.
I did not see where you mentioned the physical size in feet of your coop. It's not just the square feet, quality of the space has something to do with it. Can the immature ones avoid the older gals? If the roosts are high enough that the hens cannot peck their feet the roosts can be a good thing. But if your coop is so tight the immature ones can't avoid the older hens it just might not work for a while.
If it is pretty dark in the coop at night, the hens aren't going to leave their roosts just to be brutes. You can try putting the younger ones in there after dark and be down there at daylight when they wake up to see how it is going. You may find ti isn't all that bad or you may find it is a war zone. My coop is fairly big and has hiding places. This kind of stuff isn't an issue for mine since I added that juvenile roost to keep them out of my nests. But your flock is different from mine and your coop is different from mine. I can't predict how it will go for you.
Good luck!