Seems like the younger one are still too fearful of the older one to be in the run (close quarter) with the older chickens. It is odd because the young and old share the same coop yet the young one still is fearful enough to not share a run.
Are you able to close off the coop after all the hens had laid? If you can do that, force the young chicken out then close off access to the coop after all the hens had laid. Also open up the run so there are more room for the young chicken to hid from the older chicken. At night open up the coop to let them in. After 2 or 3 days, the coop door does not have to be close anymore, except for at high time.
As for the food inside the coop, I would continue having food inside and outside of the coop (sometime I'm too busy in the morning with kids to open the coop door in a timely manner).