What you have with a two month old male is not a rooster, but an immature cockerel that has not hit puberty yet. Mature flock dominant roosters tend to take care of the young chicks, not harm them. I've never had a problem with a mature flock master harming young chicks. I have had issues with immature cockerels and pullets trying to harm them. Sometimes mature hens can be a risk. You don't get guarantees with living animals and their behaviors, but a mature flock dominant rooster is more likely to ignore the young chicks if he doesn't actually try to take care of them than he is to be a chick-killing demon. But treat that immature cockerel as a danger, he is.
You have two different integration problems, the cockerel and the young chicks. What might be the best way forward in either will depend some on how much room you have and how you manage them. How big, in feet or meters, are your coop, run, and maybe brooder? How are they connected or situated? Photos might help. Do you free range? What is the make-up of the flock you want to add them to? How many males and females? What ages?
I regularly integrate 5 week old brooder-raised chicks with my flock of a mature rooster and adult hens, often with immature cockerels and pullets in with the flock. I have a lot of room, I consider that very important. My coop is 8' x 12. The area outside has over 100 square feet per bird, nothing like that 10 square feet you might read about as being enough. My see-through brooder is in the coop so the chicks are raised with the flock. When the time comes, usually at 5 weeks, I just open the brooder door and walk away. That's how complicated my integration is. The chicks form their own sub-flock and avoid getting too close to the adults but the adults don't go out of their way to bother them. I have never lost a chick to an adult doing it this way. If you don't raise the chicks with the flock or if you don't have this kind of room you could have a serious problem if you try this. Some people have hens that are brutes. We all have our own unique set-ups and management techniques. Other people do this differently. What works for me might not work for you. That's why knowing what you have to work with can make a lot of difference in how we might suggest you proceed.
Thanks for all the information. I'll keep you posted.
That 8-week-old cockerel could be a bit harder. I regularly have cockerels of various ages ranging with my main flock, but they have been raised with the flock and I have room. I also have many more than one, usually around 20 pullets and cockerels of the same age combined. One issue with a single bird is that chickens are social animals, they really like to be around other chickens. But if an immature chicken, male or female, tries to hang with the adults it is likely to get pecked. That's practically always a hen by the way, hens can be really brutal. The younger chicks may be terrified of him.
It's possible, especially if you have room, that you can fence him next to the flock for a week so they get used to each other, just turn him loose, and things will work out. They often do. He may stay by himself, he may be able to hang near the adults without issue, when the young ones are out there he may be able to hang with them. It's also possible you could see some issues, maybe serious issues.
When he hits puberty and the hormones that will eventually make him an adult start flowing things are likely to get exciting. That might be at 12 weeks, it might be 20, you just don't know. Sometimes it's not that big of a deal, sometimes it is hard for the faint at heart to watch. If you have an adult male in with your flock that can make it even more exciting (and raise the danger level) if you wait until this cockerel hits puberty. Then you have rivals instead of a step-dad.
You may have a ton of experience and already have all of this planned out. If so great. But if you want some suggestions on how to proceed, the more info you can give us abut what you have to work with the more we may be able to help.
Good luck!