So the hens have free range half the day and the chicks the rest of the day? I agree they need to get integrated but obviously it doesn't always go smoothly.
When you go on vacation will there be anyone to let the flock out, like a neighbor or friend?
I really need an answer to this: Are they all free ranging for the entire day? - if the answer is no, the simple answer is you don't have space for 13 birds, as the coop is not large enough to serve as both coop and run. Even a fully integrated flock will not peacefully exist in that amount of...
Is this for the entire day? How large is the area? Details are important when it comes to troubleshooting integration issues.
You could use more clutter to provide hiding spots for the new birds: https://www.backyardchickens.com/threads/a-cluttered-run.1323792/page-6#post-25037140 The bushes...
That may be tight during integration which favors having more space, though once they're integrated in you'll probably be okay.
How large is the run, or do you free range all day?
45 sq ft total, or 45 in coop, or 45 in run...?
How many birds total?
Just right off the bat, I'm going to assume the issue is overcrowding, but I'll wait for further info to assess.
Can you take some photos of your set up from further back? Multiple food stations are great, but there needs to be clutter breaking up line of sight so bully birds can't easily see that there's other birds at the other stations...