My friend had a mare with TERRIBLE seperation anxiety for quite a while and we tried the obvious with her...
Put her in a stall and keep the gelding in the field. Give her a flake or two of light hay and give her a good groom. I actually used to keep the horse in the stall and me and my friend would go inside and make a sandwich, then come out to the barn and eat lunch with the mare, pet and love on her for a while, then turn her out. This would teach her that it isn't so horrible for her to be alone with a human instead of a horse. We would do this just about every day we could, and then we would progress to getting on and riding her alone without any fuss from her. You could do this with the gelding too, just to show her that it's not just her that this is happening to.
Basically, we tried to keep her at this until she didn't care what kind of company she had, (horse or human) as long as she had someone with her.
Hope this helps! Good luck