It all depends upon your predators and how determined they are.
For almost 3 years I got away with just locking my run doors and left the pop door (coop door) open so the birds could let themselves out in the "prison run" (while I gained a little extra shut eye)....then I'd go out and open the run gates to let them free range.
Then I had a kill by a coon in the nest box. So I locked up for awhile.
After a few peaceful years, I had a coon take 3 of my best hens....one night after the next as he figured out how to can opener my run....so now I always lock the birds in the coops. However, you may not need to.
It is hard to tell in the photo, but I think 4 hens probably pretty well maxes out your coop...what is it supposed to hold? About 3 to 4...6 if bantams?
Silkies don't always want to roost on a bar. Many like to nest and sleep on the floor (especially your broody girls). You may be able to create a "downstairs" for them below your barn coop that locks.
Anyway, if your outside larger run is secure enough, then by all means, put everyone in the little red barn (if big enough) inside the larger run and let them have access to the larger run.
LofMc