the coop and run are large enough for 12-14 chickens and they have a large fenced "backyard" that they can access from a door off the run so space I don't think is a factor.
In feet or meters how big is that "enough for 12 - 14 chickens"? By my count 9 + 4 equals 13 and integration often takes more room than they need once they are integrated. Also, it is not just pure square feet per chicken, the quality of the room makes a difference. Can they break the line of sight or are they always in eyesight of each other. Photos could help. And how big is that cage?
They got attacked a bit but it seemed normal from what I have read. The second day of them together, I put them together in the coop at night. Everything seemed fine. Next day, same thing. Again at night put them together. Next morning still not bad, Reds kept to them selves and the little ones kept together, little pecking here and there. I left for work and had a friend check on them. He found the Reds chasing and fighting the little one very aggressively. Then 3 of the Reds pinned the little one down and was full on pecking, ripping feathers out and looked like they were ready to kill her.
I'm not sure what happened to change things. One way chickens live together is that when there is conflict the weaker runs away if they can. They usually learn very quickly to avoid the stronger. I often see this when integrating younger chicks, which I usually do by 5 weeks. If the younger invades the personal space of an elder they often get pecked. Each flock is different, some allow more intermingling than others, but it usually doesn't take long for the younger to form a sub-flock and avoid the older ones day and night. I have over 3,000 square feet outside and weather they can be outside all day every day when they are young so it is easy for them to avoid during the day. My 8'x12' coop has several hiding places and different places they can sleep so they can avoid the elders as they are settling in to sleep. In the morning it is usual to see the younger up on the adult roost while the adults are on the coop floor, a easy way for them to avoid. When I have an even younger third group of chicks they may be hiding under my lower nests which are just off the coop floor, avoiding the adults and the older chicks.
I'll repeat. It's not just a square feet thing, the quality of that room is important.
they have a large fenced "backyard" that they can access from a door off the run so space I don't think is a factor.
What this looks like could be interesting too.
Then 3 of the Reds pinned the little one down and was full on pecking, ripping feathers out and looked like they were ready to kill her.
With conflict, when a weaker one cannot get away the stronger doesn't know it won and keeps attacking, usually going for the head as that is where they can more easily kill it. The weaker often hunches down and tries to protect its head. When this happens there is real danger of serious injury or death. From what I've seen it's usually just one hen attacking but sometimes the others join in, sort of a mob frenzy.
I wasn't there to see it so I could be wrong, but what it sounds like to me is that one of the chicks got caught against a wall or fence and could not get to that door off the run or to some other safe place to get away.
So what can you do? If we knew better what you are working with we might be better able to offer specific suggestions. Adding clutter to give hiding places and escape routes might help. Having widely scattered feeding and watering stations can help. Housing them across wire for longer time periods might help though it is interesting that they were OK for a couple of days before this problem. Something happened to set them off and it could happen again.