Some people can keep their horses in small areas without any major issues but that's not always the case. As dbararabians has said, usually the recommended size for keeping horses in a herd is one acre per horse. This isn't just for grazing maintenance but also because horses need space to be apart. Horses naturally respond by moving away. So if the lead mare chases the new mare the natural thing for her to do would be to run away and then be kept away for a period of time. That can't happen here. Sometimes people do have to keep their horses in a small area, but often that means yarding them alone or being very selective about who is kept together.
Another thing that might be playing a factor is that your horses are pretty cooped up. I know that when I've had a horse stabled they need to have the opportunity to really get out and run everyday, whether that's in a good sized turnout or under saddle. Perhaps if all the hores get out and expend some energy they'll be more settled in their area.
In a pinch I'd tape off a corner of the area and put the horse in it, maybe giving them an opportunity to get to know each other a bit better over the fence. Then introduce them for shorter periods of time, maybe even just together and put the others in the fenced off yard.