I have two hens that are "caution" broodies: they are horrible about chicks that don't match the others and will kill them. One hen killed three on her first clutch: her first-hatched chicks were yellow with chipmunk striping, and when new ones hatched out that were brown or blue, she went completely berserk on them. The other hatched out four bantams, which she loved, and an EE cross, which she killed. I
don't like this behavior in a broody, but I can get around it if I'm very careful to only give them "color-coded" eggs that will hatch out uniform chicks.
Thank goodness we have other broodies that aren't like this!
The chick with the object on its rear has probably not finished reabsorbing its yolk sac. If the mother was going after it while it was resting in the shell, then it didn't get the time to reabsorb. You will want to make sure the other chicks don't pick at it, so separating it or giving it a diaper may be best. If you separate it, you can set up a mini-environment that is more humid than the regular brooder; that might be helpful, considering that when the chick is resting in the pipped egg waiting to reabsorb its yolk, that's a humid environment.
Unfortunately when a chick comes out of the shell before it was quite ready, it's a bit of a gamble whether or not it will be OK. Keep an eye on it, and good luck!