Sounds like those younger chicks are all together so you have already been through one successful integration. Now the trick is to go through another one.
There is no one right way to do this where every other way is wrong. A lot of this depends on how much room you have, your facilities, your management techniques, and the individual personalities of your chicks. Each flock has its own dynamics and yours will keep changing as the chicks mature. Different chicks mature at different rates too so that can mess things up. Occasionally there are disasters but a whole lot of us integrate chicks or chicks and adult chickens all the time.
There are a few things going on with your chicks and in most integrations. Chickens are flock animals and can recognize other members of their flock. Some chickens, not all chickens but some, will attack strangers invading their flock area. This doesn’t always happen and it’s usually just one or two chickens but sometimes they get caught up in a frenzy when they see one doing it. This is where housing them next to each other behind wire can make a lot of difference. It doesn’t always work but usually if you keep them behind wire where they can see each other without fighting they often accept each other’s right to be there. A week is usually enough but longer is better. Some chickens can be pretty hardheaded.
Then there is the pecking order. Each chicken in the flock has to know its position in the pecking order. There are certain benefits like prime places on the roosts or other social interaction to the chicken higher in the pecking order. Once they work out the pecking order the flock usually is very peaceful but working out the pecking order can sometimes be pretty violent. Sometimes it goes so smoothly you hardly notice. What often happens when two chickens meet that do not have the pecking order settled is that one chicken will peck the other or somehow try to intimidate it. If one chicken runs away it is settled, though there may be some chasing and follow-up events. If one does not run away (usually they do run) them you can get a fight. Usually these fights don’t last long before one of them decides running is a pretty good idea but occasionally one is seriously injured or killed. The biggest risk is when a chicken cannot run away. If space is so small they cannot get away or they are trapped against a fence or in a corner, they may hunker down and try to protect their head while the winning chicken keeps attacking (usually the head) because it does not know it has won. Lots of room when you are integrating is very important.
When you have immature chickens like yours maturity has a lot to do with it. A more mature chick or chicken will outrank a less mature chicken every time regardless of size, sex, or breed. When you integrate younger chickens in your flock they often form a separate flock until they mature enough to force their way into the pecking order. With pullets that’s usually about the time they start to lay. Until then they tend to avoid the older chickens. You might find the younger ones up on the roosts in the morning while the older ones are roaming the coop floor until you let them out. Or they just hang out in different places during the day.
Occasionally you have a chicken that is a brute. Females are just as likely to be a brute as a male. Sometimes I think they are worse but I’ve seen both. I’ve never seen a mature dominant rooster do this but immature cockerels certainly can. I really don’t see much of this but sometimes one chicken will go out of its way to seek and destroy weaker flock members. If you happen to get one of these you are likely to have problems. This is the kind of problem I solve by permanently removing a chicken from my flock but some people fight through it. A lot of times integration goes so smoothly you wonder what all the fuss was about but this type of chicken can cause real problems.
So what can you do to improve your chances of success? First, house them side by side for a while. After you are comfortable the younger ones are all old enough to free range, let them out to range with the others when you can watch. For the first two or three times I’d keep the older ones locked up so the younger can get used to that area on their own, then let them mix. There will probably be some initial curiosity and maybe even a little initial pecking if they intermix, but very soon the younger should start avoiding the older. The older probably won’t pay them any mind unless their personal space is invaded. This is what I do and it practically always goes really smoothly. I’ve never lost a chick to an older flock member doing it this way.
At night the younger chicks will probably go back to their home and the older chicks will go to theirs. Good, that is very good. Don’t force them together at night yet. I find mine are moist vicious to each other as they are settling down to sleep. That’s when the pecking order rights get enforced. Let them get to know each other better before you force this issue. I generally move mine into the main coop with the adults when the younger are 12 weeks old, but they have been roaming together for over a month by this time. Plus I have lots of extra room in my coop and even a separate roost, lower than the main roosts, higher than the nests, and separated horizontally from the main roosts so the younger have a safe place to go away from the older ones if they need it.
Other than giving them as much room in the coop, on the roosts, and in the run as you reasonably can, have separate food and water stations. That way the younger can eat and drink without having to intermingle with the older chicks. Why force a confrontation? When they are free ranging they are OK, but in the coop and run try to have places the younger can hide from the older if they need to. That may be under or behind something so they can get out of line of sight. Roosts or perches give them a way to get away from the older as long as they are high enough the older cannot peck their feet from the ground.
A safe haven can be a good thing though I’m not sure you have enough age difference to make it work. If you can set up a place in the coop or run with an opening that the younger can get through but the older cannot the younger can avoid the older if they need to. As fast as they grow this is often harder to do than it sounds.
I know I’ve made it sound pretty complicated. Remember people do this all the time and usually successful. Many people would just turn them loose without doing all this stuff I’ve talked about and probably be successful. The main thing is to be flexible, be patient, and give them as much room as you can.
Room is tremendously important. If space is really tight it might be best to wait until the younger are pretty much grown before integrating them. Even then it can be really bad if space is really tight. I don’t know how big your coop and run are but with your ability to free range them at least some it should go fairly smoothly.
Good luck!