The horse that you are describing doesn't sound like an alpha horse, it sounds like an insecure horse with lack of leadership and little respect of space. The two types commonly get confused, even though they are completely different.
Leadership is something that will help you in all aspects of life. In training, management positions, and teaching lessons, I commonly refer to my experience with horses. Shedding a little light on why this horse is acting like it is will help to give you some confidence to take control of the situation.
First of all, I can not stress enough that it is not just the methods you use, but the meaning behind the methods, once you master what is behind that method, the method itself is merely time consuming. We all know that horses sense our energy, they know our anxieties and when we are afraid, they know just as well when you throw off an energy that says "I'm not putting up with any of your stuff, so get over yourself." Pushing a horse with your energy is surprisingly easy once you get the hang of it.
A "lead horse" has leader qualities. This horse is able to focus completely, remain calm even in questionable situations, and knows its job well enough to teach others. My alpha horses are my most trustworthy lesson horses with the most beginner of students. One woman was working with my alpha mare one night and I asked who was in charge, the woman replied "oh, she is definitely in charge here, but don't worry, she's showing me what to do and she's being very sweet about it, she knows I don't know what I'm doing". Think of the qualities of a good leader; they guide without doing it for you, they advise without giving you the answer, they keep you grounded when you start to lose your mind, and they give you courage when you don't think you have the strength to move forward. These are the same qualities in a good lead horse. This is what makes me think that you are not dealing with a good alpha at all, you are dealing with an insecure horse with something commonly referred to as "bully syndrome".
The insecure horse is just like an insecure person. It is often overlooked that an insecure horse is reacting out of weaknesses in its body that most people can't even see. The body, as the horses only vessel of defense, is very important in the response time and the strength available to react in a situation. Many horses can handle when this is weakened, some can not. The weaker the body, the higher the standards are going to be for the potential leader of the horse, be that leader equine or human. Even if the horses body is in good shape, insecurity can be caused by poor socialization, poor leadership throughout the horses life (we learn to be good leaders from good leaders), or even anxiety imposed by certain people.
The way that horses deal with insecure horses is very different from how a person would think. When an insecure horse is turned out with a good herd, that horse is cast out of the herd until their behavior is appropriate. The herd is not overly violent, but they will prevent the insecure horses from penetrating into their herd because that insecure horse would be more of a weak spot in a good herd rather than contributing to the strength that the herd already has. The true lead horse remains completely composed and the insecure horse will either remain on their own, or begin to change their ways.
You have approached this horse already thinking that he is a force to be reckoned with..... 1 point for him. Next time you approach him, look at him as if he were a person. Would you look at a hyper, unattentive, unadaptable, poor listening person as a leader? Definitely not. You are dealing with someone who is so insecure in their own skin that they are going to lash out at everything to make themselves seem scarier than they are as a method of defense.
If you want to be the Boss Mare, then be the better leader, stay calm, keep your attention on the horse, listen to every move he makes, and never move out of his way. Remember, the one that is in charge is the one who is controlling where the feet move. Always protect your personal space with as much force as he requires to respect that space. For every one step he takes into your space, he has to take multiple steps back, as he has to earn the right to be close to you. Remember that the lead horse is not going to lower his or her standards for anyone, they will not make exceptions on what level of respect is acceptable. You need to be everything that you want him to be. You have to be all of those things strong enough that he can't help but feel anything but safe in your presence. Once he feels safe, he can let his defenses down.
When you approach him, look at yourself as the strong one, look at him as the insecure bully that is testing their boundaries just because they are looking so desperately for that line that they have always been able to cross. Remember that a true leader never has to go out looking for followers, others will want to follow because of what that leader has to offer. When you are with him, pump youself up, just remind yourself how lucky that horse is to have you as his leader, that is if he is respectful enough that you will allow him in your herd.