The chicks shouldn't have access to her layer feed as their calcium needs are much different at this age. And they need to have their starter feed accessible at all times, so keep them separate, and protect the chicks' feed from the hen by keeping it in their "panic room" pen where they go to be safe from her. That's half the reason for having a safe area for the chicks - so they don't get frightened off from eating the necessary amount of food they require for healthy growth.
My first "panic room" was a temporary pen in one corner of the run with a little hole in it the big hens couldn't squeeze through. Since then, I discovered it's wise to provide at least two entrances in case the hen is standing in front of one of them.
Your chicks will be much happier moved into larger quarters and having the entire run to play in. But please do find the time to rig a panic room for them. Then you won't have to worry they're getting cornered and pecked.
To teach them to go into the coop at night from the run, you need to first teach them to come to you when you call them. Using treats expedites this lesson. Use the same verbal cue each time you offer a treat, and soon they come even if you have no treat.
On the second or third night after you move them into the coop, at dusk get inside the coop and call to them. It's smart to wait until they are making those bedtime peeping noises, and are milling around nearby. Also find a small flashlight to light up the area just inside the pop hole so the chicks can see clearly where they are going.
You may need to show them a treat to entice them to come inside the first time. Once you get them in, close or block the pop hole so they don't turn around and run back out. Then go about placing them on the roost, but don't spend more than two minutes. If they don't stay roosted, give up and try again the next night.
It'll take three nights to a week for them to learn to go inside at dusk on their own, then perhaps two or three nights of perch training to begin roosting on their own. Some chicks are immature, and you may need to forget perch training for another couple weeks if they aren't beginning to roost on their own after three or four nights.