I have read through all the the thread and think I understand what it going on and what you are trying to do. While I think your on the right track I don't think tying them is the answer, when they are tied they have to much time to react and what you need to do is get them thinking. And feeding one and not he other is never a good idea, it is very stressful and since they don't reason, hold a grudge, or premeditate I cannot see it working. The best way to get them to think is moving their feet, make the right thing easy and wrong thing difficult. Make them uncomfortable for doing the wrong thing.
If the mare is not your responsibility then she should not be your concern to fix. You need to focus on your horse and he needs to respectful of you regardless of what the mare or any other horse is doing. I would not tie the mare, I would just not worry about her. Work your horse near the mare where you can work him in site of the mare, hustle his feet and get him breathing heavy make him want air. Take him away from the mare to rest, let her do whatever she is going to do, remember not your problem. If your horse starts acting silly and wants to back to her then take him back and work him some more hustle his feet, when he wants air take him away to rest. Eventually he will figure out being near the whiny mare gets him nothing but work and he will be happy to ignore her. It may take a couple sessions but he will figure out being away from her is much better then being near her. Now if you really want to help the mare get over her issue, and you have the space, and your able you can ride your horse in with the mare but chase her around make her move her feet and get her wanting air. Then leave with your horse, if she starts yelling go back and chase her some more, both horses will decide that is best to be apart because when they are together they have to work.
Horses are herd animals, safety in numbers yadda, yadda. So I get the mares anxiety, and it only takes one horse to upset a barn. What you need to do get your horse to look to you as his leader and ignore the other horses when he is with you. If you plan on showing, trail riding no matter what you plan to do your going to run into other horses and your horse needs to know he can look to you for safety and direction. Get him to see you as his herd leader, by moving his feet, and his wanting to run back to the other mare will go away by itself. Good luck to you.