I had one bird who would go a bit wobbly like you describe, she always recovered after a few days though, I just recently had her pts at the age of eight, but it wasn't conected to her wobbly turns.
I've had loads of birds have a mucky bum, very few of them died, most just needed a pro-biotic, I use Protexin powder which can go in food, it's intended for cats and dogs but works very well with hens.
As to the bullying, I recently got three more hens to solve severe bullying of one hen, worked a treat, she was boosted up the pecking order and is much happier having hens below her.