The run is where most interaction among chickens occurs. The coop is generally where chickens sleep at night and lay eggs. Unless you have no run, the run is what you need to focus on as far as integration of two different age groups.
I've found the best way to integrate new chicks with older chickens is to brood the new chicks right in the run itself inside a safe pen. Chicks growing up in proximity to the other chickens are accepted very early and integration is much easier than introducing the two age groups later on.
When the new chicks are two weeks old, chick size openings are created in the chick pen so the chicks can mingle with the older ones. However, the openings, while allowing the smalls to find refuge inside, are too small for the larger chickens to get through. Food and water is also in this safe space so the smalls don't have to compete with the older chickens.
Around age five weeks, when the chicks are finished needing heat, they can move into the coop to sleep. Since chickens usually are focused on roosting and sleeping, there's not much conflict to be expected. I keep the safe pen, I call it a panic room, until the chicks get too big to fit through the openings.
