Welcome to the forum. Sorry but this may get a little long. You have two different issues.
First is brooding them. I don’t know where you are or what your weather is like. That can have an effect, but I’d guess you are still seeing pretty cool temperatures outside. What chicks need in a brooder is food, water, protection from predators, protection form the elements, and in practically all conditions, a heat source. None of this absolutely says they have to be in your house. I built a permanent brooder in the coop. I have 22 chicks in it right now about 1-1/2 weeks old that went through outside overnight temperatures in the single digits Fahrenheit. I kept one section of that brooder toasty and the food and water pretty close to that heat source but some mornings the far reaches of that brooder were frozen. I consider the older chickens in the flock as potential predators at that age so they are definitely locked out of the brooder.
I have no ideas what facilities or possibilities you have. If you have a garage or other outbuilding that provides decent weather protection, you can set up a brooder out there. It depends on how predator-proof that building is as to how solid you need the brooder to be. Many people just get a large appliance box and use that. If they outgrow it, get another one and tape two together.
You might read my post in this thread for help in deciding when they don’t need any more heat.
https://www.backyardchickens.com/t/860561/can-my-chicks-go-out
Your other problem is integration. You’ll read a lot of different things on here about when you can integrate them. That’s because your facilities play a huge part in what can work for you. We are all unique. The way I do it could be a disaster for others. Some people consider me way too safe. One basic rule to remember is that chickens usually solve disputes by the weaker running away from the stronger or avoiding the stronger to start with. That means they need enough room to run away if they are chased.
Chickens can recognize which chickens don’t belong to their flock. It doesn’t happen all the time but occasionally one will attack an intruder. A way to really reduce the chances of this happening is to house the chickens next to each other for a week or so before you let them mix. None of this stuff comes with absolute guarantees since you are dealing with individual living animals, but I do recommend housing them side by side with a wire fence separating them if you can. Some people can’t and it still normally works out.
Chickens, like other social animals, set up a pecking order so each chicken knows its place in the social order of the flock. When two chickens that don’t know what that status is share personal space, one normally tries to intimidate the other, often by pecking. If one runs away, they’ve settled it, though there may be some chasing involved or a repeat performance. Occasionally they are fairly evenly matched so it takes some skirmishing to settle it. On really rare occasions they may fight to the death but that really is rare. The biggest danger in this is when a chicken cannot run away. If it can’t get away, it may just hunker down, quit fighting, and take the punishment. The winner doesn’t realize it has won because the other did not run away so it keeps attacking. That is why space is so important.
The last key to the puzzle is that mature chickens always outrank immature chickens and are often not shy about enforcing those pecking order rights. That’s why you usually see a group of younger chickens form a separate flock. They are simply avoiding the older chickens.
The younger the chicks the more danger to these confrontations. This does not mean that every hen will automatically seek out to destroy any chick they see. Some of my broodies keep a pretty tight rein on their chicks and keep them close but some allow their chicks at two weeks age to mingle with the flock. Usually the older hens ignore the chicks but if they invade the elder’s personal space, they might or might not get pecked. If they get pecked the chick runs back to Mama as fast as those little legs can carry them. Mama ignores this. That chick needs to learn proper flock etiquette. But if that hen chases the chick, Mama immediately teaches her that’s not really necessary.
I’ve had a broody totally wean her chicks at three weeks and leave them to find their own way with the flock but she had spent three weeks teaching the others to leave her babies alone. My brooder and grow-out coop are where the adults can see the chicks as they grow. I have lots of room and turn my chicks loose to mingle with the flock at 8 weeks. I’ve never lost one doing it this way. If space is really tight, you might need to wait until the young ones are practically grown before you integrate, and even then if space is tight you can have issues. Different things work for different people.
I’ll end my rambling by saying that I’ve never had a problem with a dominant rooster. A good dominant rooster takes care of all his flock members. It doesn’t happen every time, but I’ve seen a rooster go take care of chicks if they get separated from Mama until she can figure out the concept of “gate”. They are living animals and I’m sure others have had issues with roosters but I never have.
Good luck with it and once again, welcome.
