The thing with a stud is that they should be expected to behave like a regular horse, except with even better manners, with no exceptions. They should never be allowed to hollar at another horse, pay attention to another horse, drop, be pushy, etc. I don't care if they are under saddle, being shown in hand, or are tied up at the trailer. Taking him by himself might be easier so he won't have something to be territorial over or to be attached to. You will have to find your own method of correcting him - we can't tell you any exact way to do it, every body has their own method. But whatever you do, be firm, be consistent, and when he corrects himself, reward him - not with treats, but with releasing whatever pressure you were putting on him.
At the same time, don't put him in a bad situation. Don't put him next to a mare in heat, don't put him in the center of a big group of horses - stand a few feet away. Know where you are in the arena so you can have an escape route and know how he responds to you and your corrections.
As you can tell I have been around quite a few studs. My family bred for years, now my brother is doing the same but on a smaller basis. Our studs have usually been the best mannered horses on the property because we demand it of them, more so than any other horse because they, more so than other horses, can be so dangerous if not properly handled. If it is engrained into them, though, they can be some of the best horses you have ever owned. One of you best studs (production wise) was also one of our best HORSES - in the show ring, and also to teach beginnners to ride, both at home and away from home. One of those rare beginner/kind soles that no body would believe was a stud, and if they looked, didn't care at a show that a 13 and under was showing because you would never know.
Good luck with this one but be careful as well, and get help from someone experienced with studs if needed.