This is a great question and you have given me lots of detail to help in forming a response. I like to define a ‘broke horse’ by saying that you have full control of direction and impulsion. This is not just one question but three separate questions, with three separate answers. They have to do with (1) attention span, (2) contact, and (3) speed control. These questions don’t surprise me with ex-barrel horses. In this discipline it is about time and speed, there is no need for collection. I appreciate your question about collection. To many people, collection is unnecessary and they do not feel it is important. The simple answer to your questions is that your horse is resistant, is lacking knowledge, and respect.
First, I would like to reply to your statement about your horse being distracted and inability to concentrate. What is the length of time a horse can concentrate? The answer is the same length of time “you” can concentrate. Think about this, if you take your attention off of the horse, will the horse continue to concentrate on a certain task? NO! Ask yourself, who is the one distracted by the bit? Don’t worry about all the fidgeting with the bit; that goes away over time.
Second, “accepting of the bit”; contact or no contact, what to do? This is where she lacks respect and is resistant. If a horse is not quiet with the bit, you don’t use it less but more. Think about this, if your horse is worried about a plastic bag, do you never show him one? NO! You desensitize him to it by repeatedly introducing it to him while raising the response (usually fear) and waiting for the correct response (quiet acceptance). The purpose of the reins and bit is to communicate to the horse. You cannot successfully communicate if you always have resistance to the bit. If you practice lateral bending, serpentines, side-passing, counter-bending, hips-in, shoulders-in, leg-yields, and more exercises, she will learn to calmly accept the bit over time. All these exercises require you to pick up the reins and ask her to give and move a body part. Your reins are like picking up a phone and calling your horse to communicate.
Third, “slowing her down”; this is where she lacks knowledge. You said that you reward her when she slows down, I would like to know how you reward her. Let me see if I can help you understand a fundamental principle. Your horse has been taught to run, but now you are asking her to slow down. She does not know it is wrong to go all out. Two things need to happen first, you need to think slow and raise and lower her response. Go find yourself an open field so you have room to maneuver. There are a couple of ways to approach getting her slowed down on the trail, but it takes preparation and the understanding that anytime. When you move a body part or change direction you can slow the horse down. If your horse is familiar with a couple of maneuvers then you can use these maneuvers on the trail to slow her down. The key is to make sure your horse knows the maneuvers and is not worried about the maneuvers themselves. If you have control of the shoulders or hips at the canter, you can do hips-in, reverse-arcs, and leg yields to get her slowed down. The other way is to change directions, but this will require lead-changes or counter-cantering. These are two ways or strategies to slow her down.
There is a third way, and it is my preferred way, but it requires you to build a cue to slow down (slow-down cue). The cue will be the outside rein and leg. Simply put this is called a reverse-arc at the canter. You bend the nose to the outside using your outside leg to holder her and keep her from changing directions. Make sure you have her on the correct lead first. You’re causing her to be out of balance and slightly uncomfortable, she will begin to look for the answer, the reward or the release. Once she finds the answer (i.e. slow down), put her back to straight. By using the reverse-arc to slow her down, you keep her going forward and her ribcage straight. This cue builds a slow-down cue on the outside rein and leg. I particularly like this method because it is a solid cue in conjunction with your seat and rein. If you were to do lots of roll-back and speed transitions to slow her down from canter to trot and back up again, you could possibly take the forward out of your horse and create another problem entirely. Keeping your horse going forward is one of the most important things you can do for your horse and to keep riding safe. Hope this helps you get a clear perspective how do work with your mare. Randy Byers Horsemanship