I don't know how much this will help since I am new to all this myself but...
We came home with 4 fluffy butts 2 months ago & were keeping them in one of those indoor rabbit cages... we thought it would be plenty of room but after a week (they really do grow quick!!!) I had the same thing going on that you do... one poor little chick (GC) was getting picked on by another- drawing blood & causing the other 2 to peck at it also. To protect the GC, I removed it from the cage but I didn't want the other chicks to look at this one as a stranger when they were finally ready to go outside so I took some short fencing & jimmy rigged a small caged in area, attached to the rabbit cage but divided by the cage wall. At night I would then place the GC back into the rabbit cage so it could sleep with the others. This seemed to work well so I wondered if it was a space issue (were the small fluffy butts feeling to confined in the cage) or did they just not like the GC that had been picked on. So every day, I would take out a different chick & place it in the homemade cage & see if anyone would pick on the GC. As long as there were only 3 in the rabbit cage, the GC never got picked on. Even though I thought it was enough space, the chicks obviously did not agree. All 4 are now back together outside in their large coop/pen & haven't given me a single issue.