For a mixed Laying/Young Bird flock I feed Grower with Oyster Shell offered separately. The ones that need the calcium to make eggs eat the oyster shell. I've seen the young ones take a bite or two but don't eat enough to hurt hemselves. It's usually that they try it when they first see it them leave it alone.
I agree with housing them side by side for a week or so with wire separating them, then let them mix with as much room as you possibly can. Start out with them mixing under your supervision and pretty soon you will have a pretty good handle if you need to be there or not. Instead of moving them back to their coop at night, if you can fix a safe place for them to stay at night in the run but separate from where the older ones sleep, it will work out better. That way, when you totally mix them, they will each go into their own coop at night. Bedtime is often one of the most vicious times for mixed flocks. At other times the young ones can more easily get away. If you cannot house them separately, I suggest you make sure you open the pop door very early so the young ones are not trapped in with the older ones with no escape route after they wake up.
Something that I find that helps is to set up separate feeding and watering stations. The older ones will often keep the young ones away from food and water, sometimes to the point that it is downright dangerous to the young ones. Either they don't eat and drink enough or they get attacked when they approach the food and water. You will notice that the younger ones are scared silly of the older ones. That is normal and called self-preservation.
I appreciate your not wanting the young ones to get hurt. There is a difference in establishing a pecking order and a chicken being injured. They establish the pecking order by intimidation. The more dominate one will approach, bluff, or peck the heck out of the weaker one. The intimidation is accomplished, the chickens go their separate ways, and the flock becomes relatively peaceful when they all learn their proper place in the flock. Occasionally you get a Matilda the Hun that will actively search out to destroy. Or that intimidation peck can actually draw blood. Then the integration does not go well. Most of us manage to integrate chickens without serious problems, but the process is not without risk.