I have a different take on it though the final answer may be the same for you. I integrate brooder-raised chicks at 5 to 8 weeks of age all the time and have never lost one to another adult member of the flock. But my circumstances are different from yours.
My brooder is in the coop. The chicks go in there straight out of the incubator, even if the outside temperatures are below freezing. Although they are isolated, they grow up with the flock. Normally at 5 weeks I move them to a grow-out coop and run adjacent to the main run. They still see each other. Once they are fully adjusted to the grow-out coop, usually 8 weeks, I let them mingle with the adults but they go back to the grow-out coop to sleep. Normally at about 12 weeks of age I move them or some of them into the main coop to sleep at night. There can be different reasons for that. Occasionally if I have too many for the grow-out coop I leave some in the main coop to start with, just opening the brooder door and let them mingle at 5 weeks. They are fine. I’m not real consistent in what I do because each brood is different and circumstances or weather may be different. But somewhere between 5 and 8 weeks is normal for my brooder raised chicks to mingle with the flock during the day. I’ve had broody raised chicks weaned anywhere from 3 to 9 weeks of age and left to make their own way with the flock. I’ve never lost one of those to another adult either.
I have a rooster, a mature flock master. If a rooster is introduced to chicks when they are pretty young he sees them as his offspring, not rival chickens. Not all roosters are the same but he will often help protect those chicks until the boys are old enough to become rivals. The pullets are members of his flock always. I don’t know how much this actually helps but I think it does some, at least with some roosters.
Now the really big question, how big is that “large” run? I’ve since expanded this space but I used to have a 12’ x 32’ main run plus 35’ x 65’ enclosed in electric netting. One way chickens have learned to live together in a flock is that the weaker run away from the stronger and then just avoid them to start with. Young chicks are always at the bottom of the pecking order. They quickly learn to form a separate flock and avoid the adults. They have to have enough room to stay away from the adults or it can get really bad. It also helps to have separate feeding and watering stations so the young can eat and drink without having to challenge the adults. I keep three separate ones, one in the coop and two outside.
I’ve never had a pullet challenge an adult laying hen for pecking order rights when they are the “same size”. It’s not just size that is important but maturity. Mine don’t work their way into the main flock until they mature enough to do that, normally about the time they start laying. Until then they form their own separate flock. They may mingle with the adults some and even sleep on the same roosts but don’t really get comfy-cozy with them. Even on the roosts (which are also plentiful) they separate into different groups. But I have never tried to integrate practically grown pullets with the main flock in tight spaces. Mine integrate a lot younger and have a lot more space. With different conditions you will see different things. I’m sure most people are successful integrating when they are the same size, which is often given as 16 weeks of age.
It is not at all unusual for older hens to be pretty brutal to a young cockerel, especially the dominant hen with no rooster in the flock. She seems to recognize that he will eventually be a rival for the dominant position so she tries really hard to keep him in his place, subservient to her. This can get really vicious. She will often go out of her way to find him and attack, especially around the head. This can be pretty rough, even if he has plenty of room to run away and avoid. In tight spaces this can sometimes lead to his death. Even in large spaces there is risk but usually it is not fatal. They are living animals, each with their own personality. Sometimes this transition of leader ship from hers to his is pretty peaceful but often not.
If your space is tight at all, waiting until they are a lot older may be required. The tighter the space the harder integration is. For some people waiting until they are the same size is a very good idea. Even then you need to watch them.
Your cockerel presents some special problems. There are different ways you can go about it. I don’t know how bad that hen’s attacks on him really are. Her beating him up some is not unusual. With a decent amount of space and the opportunity to avoid her they may work it out. With you gone I’d be nervous trying that. You can try isolating the head hen and then try integrating the others, cockerel as well as pullets, to see how that goes. It may go great, maybe not. Isolate the head hen long enough to knock her down from being the head hen. Five days will probably be long enough but make sure the others are doing OK without her. When she gets back she will be so busy working her way back into the pecking order that she might ignore the pullets and cockerel. She may not make it back to head hen status again either. Another hen may keep that position from her. You are dealing with living animals so no one can guarantee you any specific outcome.
Another option is to keep the cockerel isolated until he matures, maybe 6 to 7 months of age or even a year, before you try to integrate him. Once he matures enough to dominate that lead hen she should accept his authority and may become his best buddy. But don’t be surprised to see him chasing her and being fairly brutal to her a day nor two until she does accept his authority and dominance.
You can try integrating the pullets without the cockerel, either now or when they have grown some more. It may or may not work out. You might need to keep them with the cockerel until they all mature some more.
If you isolate the cockerel and pullets together until they mature expect it to get fairly rough where they are, especially if space is as tight in their space as it sounds like from your post. During adolescence the cockerel will mature faster than the pullets. He will probably start forced matings to establish his dominance over them. The more immature pullets will not know what is going on and usually resist, which causes him to be even more forceful. Even with more space this phase is often not for the faint of heart to watch. If you can stand this phase they will normally work their way through it as they mature and become a really peaceful flock where everyone knows their proper position in flock society but occasionally pullets get injured during this phase. It’s fairly normal for the pullets to spend a lot of time up on the roosts or in places where they are away from the cockerel. The more space you can give them the better.
Integration requires more than the bare minimum space. Raising a cockerel with the flock requires more space. Wait until you see the adolescent behavior. Integrating a fully mature rooster to an all hen flock usually goes pretty smoothly but there can be some conflict between the head hen and the rooster for a bit. Keeping more than one male with the flock greatly increases the space requirement once they mature.
Many of us do all this stuff all the time, usually quite successfully. Occasionally you get a brute, male or female, that just don’t belong in a flock. But I’m convinced that the majority of behavior problems on this forum are caused from lack of adequate space. That’s anything from feather picking, broodies raising chicks with the flock, integration, or rooster problems. Another problem area is when they go through adolescence and before they become responsible mature members of the flock. There can be other causes but I think these two top the list. Space may or may not be your problem. It’s really hard to tell across the internet. But each of us are unique. We all have our individual set-ups, each flock has its own dynamics which can change with just one chicken. You have to be flexible in working out solutions to your problems.
You can work this out but it may require more work from you or even expanding your facilities. Good luck!
