Yeah, I'm not sure if they are 3 one-month-old chicks or an unknown number of 1 month olds. Doesn't matter, my response will be the same either way. In Australia this time of year they don't need supplemental heat whichever age they are.
What you describe is pretty normal, at least to a certain extent. Mature chickens outrank immature chickens in the pecking order and are often not shy about enforcing those pecking order rights. What I typically see is that if their personal space is violated they often peck the chick to drive it away. It's bad chicken etiquette for a young one like that to bother its betters. Usually that is as far as it goes. The chicks pretty quickly learn to avoid the older ones.
But sometimes a hen will chase a chick as it runs away, not being satisfied with just pecking it. As long as the chick can get away, either having enough room or being able to run to a place the hen cannot follow, life is OK. How much room they have and how it is set up can be pretty important in this.
I find this to be really rare but you can have a hen that goes out of her way to attack chicks. Personally I've never seen that and I integrate chicks all the time, but enough people I trust on here say they have seen it that I have no doubt it can happen. My suspicion is that how much room they have could play into that but about anything can happen with living animals. It is not always a room issue, sometimes a hen is just a brute.
My goal in these things is that no one gets hurt. They don't have to play together or cuddle up on the roosts together, just no one gets hurt. That other stuff will come later when they all mature.
If we knew more about your space in the coop and outside, how they are set up, and when that outside space is available to them we might be able to offer specific suggestions. As it is I can only come up with generic suggestions. Housing them across wire so they can see but not touch for a week or much more is a good thing. Give them as much room as you can. Quality of what room you have can be improved by giving them places to hide under, behind, or over to break line of sight from the other birds. Widely separated feeding and drinking stations allows all of them to eat and drink. Do not enclose them in small spaces thinking they will work it out. They probably won't, not in a way you'd like. If they want to sleep in separate places and it is not a predator risk, let them. As well as you can let them work things out at their pace.
Many of us go through this all the time. For many of us it's not a big deal, we've worked out our procedures that work with our set-ups. But your situation is different from mine. What I do might not work very well for you. You just need to wok out what will work for you.
