My situation is very much like yours. Chickens are all different. Some are patient and accepting toward the youngsters, but one or two older ones, usually the ones lowest in the pecking order, may pick on the smaller ones. Some people just declare it's time to integrate and toss them all together and let them sort out the pecking order. But I feel better supervising.
I overdid it last year, though. I had a bully that refused to let the youngsters come into the coop at night, so I would put her in "jail", a partitioned off section of the coop, to keep the peace. It had a lasting effect on her. While taking her down from her alpha position, it sent her into a permanent molt, she lost weight, and became withdrawn. She still isn't the same trusting hen I raised from a baby.
It's a tricky balance, trying to keep the smaller ones from getting injured and traumatized while respecting the needs of the older ones.
I have six ten-week olds who get bullied by three one-year olds at roosting time. I usually stand by and referee, moving hens to different places as the need arises.
In two or three weeks I'll be moving my three youngest chicks (now four weeks old) into the coop. They are currently spending days out in a partitioned off section of the pen. There are three out of the six older chicks who bully them. It's going to take some real juggling to referee them all when this final merger takes place.
They may surprise me and all get along. I won't really know until then.
My advice to you is just keep an eye on them and don't let anyone get hurt. - This is the final stage of raising chicks - moving them into the coop and integrating them with the flock, and, to my mind, the hardest part. When they all finally reach the same size, it'll settle down and you'll get some peace.
Good luck!