Should we get rid of multi-problem hen?

Our Cuckoo Maran just can’t settle down and we are thinking of giving her away.
Her History: Of all the hens she is the only one who had a lot of trouble starting to lay, having many soft-shelled or no-shelled eggs interspersed with giant double-yolked ones. The color was not uniform (white speckles, light brown instead of dark) At this time she began systematically pulling feathers from the tails of the other hens, stalking them incessantly. Finally, we found the Austrolorpe with her comb torn nearly off and her head all bloody. The wound was very close to the eye. We isolated the Maran for one week then let her re-establish herself in the pecking order. We used a water sprayer to squirt her when we saw her starting to peck. It worked and she settled right down. Then she went broody in September after having sporadically laid eggs for only a couple of months. (She’s around 10 months). We left her alone until she ate an egg. Then we removed her from the nest and isolated her again for three days. The broodiness went away but now, four weeks later she hasn’t resumed laying. Also, she has become aggressive again and constantly rushes around the yard and confronts the others, stressing them out and sometimes pecking at them. Both the Austrolorpe and the Barnvelder have had their vents pecked clean of feathers one of them was pecked bloody at one point. The theory I’ve heard is that the Maran needs a rooster! The thing is, who will want her? And as I've read another member write, "Cuckoo is supposed to refer to the color, not the behavior!" I am very fond of my hens, but his one seems to be doing harm to the others.