Ok I have horses all my life and GW like everyone says is not going to fix this.. If horses are in pasture together they NEED a pecking order thats how all herd animals are. The head of most very herd is a female. Most likly the oldest mare is the head of a the herd. Your filly is just seeing where she stands.
I have never really seem a bully horse in a herd.. I do see ones trying to move up and the older ones defending thier place. AS far as a horse being picked on all the time, thats just who they are.. Thats why it important not to over crowd pastures ROOM to move away.. I have one little mare (miniture) who always alone.. she and her foals are always apart from the others.. the foal plays with the others but Mama's alway off to the side.. she just does not want to fight she knows her place stay out of every ones why. It a horse is not getting feed. more space at the hay rack is needed.. so if the horse moved away by others it can just move to another rack or down the line away for the horse who is not a bully just higher up in the herd.
I put the new horse in early in the morning.. in a large pasture (this gives the new horse room to get away if needed) NO TREATS OR FEED
they most always have it all worked out by night fall. If it look like the new horses is having a real hard time I might pen it up with one horse for a day and then turn both out. This way it knows at least one horse and they seem have an idea where they stand.
But for the most part it seems like the best thing to do is let them work it out.. Horses are herd animals they need the herd.. they need to know where they stand in the herd.. if they keep removing the new horse or the top horse and putting them back in the are making it a real issue everytime you put that horses back in it will begin all over again..
Everyone will have a few new bumps and bit marks but no one is really hurt.
I know there are a very few times a horse will get really hurt. But most of the time that is because there was no room for the horses to keep apart.