It sounds like things are going perfectly well. Don’t get impatient or give up hope.
A mature chicken always outranks a less mature chicken in the pecking order. If a chicken lower in the pecking order intrudes on the personal space of a more mature chick there is likely to be a peck to remind the lower ranking that it is bad chicken etiquette to intrude on its betters. Immature chickens quickly learn that and form their own separate flock that avoids as much as possible the mature birds. If the older birds are in the run, the younger are in the coop. If they are all locked in the coop the older are on the floor and the younger are on the roosts. Things like that. The more space you can give them the smoother this process goes. Extra feeding and watering areas also helps keep the peace.
Eventually the younger birds will mature enough that they can force their way into the pecking order. It’s not a matter of size but of maturity. It’s not unusual at all for a mature bantam to outrank a mature full-sized hen in the pecking order. That comes from the personality of the individual chickens once they mature. My pullets normally mature enough to make their way into the pecking order after they start to lay. That’s just a general statement, it can vary. They may also kind of form a sub-flock of their own even after they fully join the main flock but you will see a lot more peaceful interaction.
By having older hens already laying you are ahead of the game in getting the pullets to use the nests. Each is an individual so they don’t come with guarantees with anything related to behaviors, but I’ve had much better success with pullets using the nests when there are older hens around already laying to show them what to do.
When the hen weans her chicks they will already be “integrated” with the flock. The older chickens will accept their right to be flock members and should not go out of their way to attack them. That’s a big advantage of having a hen raise her chicks with the flock. But they will still be immature. They will still have the same pecking order issues that immature chickens face. They will form their own sub-flock and avoid both groups of older chickens until they mature enough to join the pecking order just like that other group. Plus you probably have cockerels with this group. When those cockerels hit puberty things are likely to get really exciting down there.
I don’t know how much total room you have, either in the run or in the coop or combined, but the more room you can give them the better. All this stuff goes better if you have more room. Keeping as much of the run snow-free as you can, maybe expanding the run if your space is at all tight, and setting up feeding stations wide apart in the run can help. Having places the younger ones can get out of the line of sight of the older like short walls or something to hide under can help expand your space. Having perches high enough that the younger ones can avoid the older can be really handy. Adding more roosts in the main coop might help. I put in a separate roost, a little lower than the main roosts but higher than my nests and horizontally separated, to give the younger a safe place to sleep that was not my nests.
Those 4 square feet per chicken in the coop and 10 in the run magic numbers pretty much applies to a flock of mature hens though you can often add one rooster to that number without a huge change, but when you integrate as much as you are you really need more room. It goes so much smoother if they have room to avoid the more mature birds.
I don’t have a clue what your coop looks like or your nests. I can’t tell you how you can add nests. They can be as complicated as you wish to make them or as simple as a box or milk crate with bedding setting in a corner.
I see nothing good coming from locking them into a tiny space and having them fight it out. That is more of a recipe for disaster. Flocks have been going through the process of absorbing new members since chickens existed. There is a natural way to do this. When they mature enough they will work it out provided they have enough room to coexist until they get mature enough to go through the process. A difference is that we often pack them into too tight a space for them to work out this process in a natural way. A lot of the time people think we have to micromanage a process that has been perfected over thousands of years. When your cockerels hit puberty you are likely to be back asking about that, what happens then is often not for the faint of heart, but in general by giving them enough room and letting them work it out with minimum interference from us is the best way to go.
Now for the legal disclaimer. Chickens are living animals, each with its own individual personality. Each flock has its own dynamics. No one can give you any guarantees when it comes to behaviors. We can tell you what is most likely to happen and the best ways to prepare and handle things, but occasionally (not that often thankfully) you get an Attila the Hun or Attilalita the Hunness that is just a brute and throws everything out of kilter. They just enjoy beating up on other chickens. But most of the time, given room and time, they work it out and you have a peaceful flock, especially when all are mature.
Good luck!