Do you ride adjacent to the pasture? I would take Dixie (when Zonie is out in the pasture) and work her close to her buddy, then trot away and allow her to rest farther away. If she refuses to rest, trot purposefully back to Zonie and work (circles, rollbacks along the fence, etc. Just keep her feet moving energetically), then allow her the cance to rest farther away again. Eventually she will understand that she gets to rest away from her buddy. If she gets to the point where she behaves, but whinnies and excites the other horses, you can trot back and work her whenever she whinnies. She will learn that if she can't be quiet, she has to work harder.
With the horse flipping out in the corral, I would get Dixie basically fixed, then just take her away and just let Zonie throw his tantrum. I battled this with two geldings. Whenever we took one to a show, we would leave the other one in his stall (we live on a very busy road, so risking an upset horse jumping his fence was out of the question) and turn out the lights and ignore him, just like dealing with a toddler's tantrum. Eventually they would scream themselves out and there was golden silence. They learn that flipping out doesn't bring "brother/sister" back. By the end of the first summer as a two horse barn, we were riding separately and turning them out one at a time
Hope that helps! Good luck!