Separation anxiety is a difficult condition to deal with in horses, as it is inextricably tied to what psychologically affects them most: fear, and herd orientation. There are a few techniques that may help, but they will not entirely eliminate the condition.
First, if it's possible to separate the horses on the property for everyday purposes, that will help tremendously. It's good and appropriate to give horses access to each other -- they are social animals, and having companions is important. However, when they become so bound to each other that it affects their "jobs" as horses, it's time to separate them.
With one of our herd-bound horses, we keep him in a separate corral away from the barn, and on a regular basis we turn other horses out with him. That has helped minimize his panic when one is taken away. The herd-bound horse should be within sight and sound, but physically away from the others (or at least away from your wife's boss mare).
Next, giving the worried gelding a big flake of hay, or a bran mash, whenever the other horse leaves the property will distract him. Be assured that the herd-bound anxiety will overrule the hunger -- but it will help a little bit, and sometimes that's the best you can do.
Daily feed-through nutraceuticals designed to calm the horses are readily available and are considered safe. Some are melatonin based; others are herbal, including valerian and similar calming herbs. In addition, there are prescription sedatives available that your veterinarian may be able to offer. Obviously, the geriatric horse such as your wife's gelding may not be as good a candidate for certain tranquilizers as a younger horse, but a low-dose sedative, perhaps given orally, may be called for. You may want to try some of these products and see if they make enough of a difference that they're worth regular use.
There used to be a wonderful natural product available called Modifer that was a calming pheremone for horses, similar to the DAP (dog appeasing pheremone) for canines. It was a nasal mist that helped greatly with anxiety issues. Unfortunately, it was taken off the market by the company that manufactured it (for marketing reasons, from what I understand, as opposed to safety problems) and I don't think it has ever been brought back. It would have been a great product for your own horse's situation.
Good luck with this frustrating situation. I know it is stressful for your horses and for their humans!
