Integration can be tricky no matter the age, it's about territory and hierarchy...there will
always be a pecking order no matter how long they've been together.
It's best to keep them separated by wire in both coop and run until they are of similar size just so the youngers are physically on a more equal footing.
Partitioning part of the coop off worked best for me. Some folks have 2 coops and split the run in half with wire.
The sizing step between brooder and coop is often overlooked..... until the chicks hit their heads on the brooder top, lol.
There are many possible solutions depending on your situation, resources and creativity.
Here's some notes I've taken on integration that I found to be very helpful.
See if any of them, or the links provided, might offer some tips that will assist you in your situation:
Integration of new chickens to flock.
Consider
medical quarantine.
Confine new birds within sight but physically segregated from older/existing birds for several weeks, so they can see and get used to each other but not physically interact.
Integrating new birds of equal size works best.
The more space, the better. Birds will peck to establish dominance, the pecked bird needs space to get away. As long as there's no blood drawn and/or new bird is not trapped/pinned down, let them work it out. Every time you interfere or remove new birds, they'll have to start the pecking order thing all over again.
Multiple feed/water stations. Dominance issues are most often carried out over sustenance, more stations lessens the frequency of that issue.
Places to hide out of line of sight and/or up and away from bully birds.
Read up on integration..... BYC advanced search>titles only>
integration
This is good place to start reading:
https://www.backyardchickens.com/a/adding-to-your-flock