my mare will brace against the bit when we get any speed. I will sit deep in the saddle and try to stop actively riding but she will brace against the bit and go go go. Not really tucking her head into her chest more of I don't care how hard you pull I am just going to keep going. I tend to have to see saw that bit to get her to respond. But a one rein stop is quite dangerous on this horse - she is literally the most limber horse I have ever ridden and can fold herself in two and still keep doing what she wants. Quite scary
When not gaiting at a slower speed even with other horses if she is in the lead she will collect beautifully and just float in her gaits. When another horse comes up beside her or tries to pass the race is on! and bits be damned!
I've ridden a few horses like this too. The horse has lost her brain at these times, and is out of control.
Was she by any chance a show horse? Keep in mind that many gaited horses, especially the show ones, are trained with the rider sitting back and keeping hold of the reins. That position to a horse means GO not whoa
Couple of ways you can try to get her brain back; if you are out on the trails and have a mountain nearby, go up the mountain until she is listening to the bit again and rather wants to stop or slow down a bit. This of course, is not always possible...
Two, get your riding companions to go around you and literally block her and ease to a stop. Again, not always easy to do.
So the third and best way, is more training, but it has to be done slowly and carefully. You need to retrain her brain to respond to the aids. Snaffle is fine for this. Big bit is not really the answer.
Begin by only riding her in an arena, without other horses. You can add them back later. Do everything at a walk and reward her excessively when she does as you ask. The plan is to retrain her brain and responses while also training her muscles to be a little firmer so she is less like a noodle! Oh yeah, and keeping you a bit safer!!
You need to ask for a nice marching walk on light contact. Do turns, changes of direction and even some leg yielding. Every time you stop her, back her a few steps. Not a vigorous back, just a few steps then stop and reward.
Then begin to change from a marching walk to a slow walk. Transitions are your friend. Reward every try. Continue this path until you are making transitions between the gaits and within the gaits.
Do not make tight circles as this can trip and upset a gaited horse.
You must teach her (gently) that their is more than one speed.
Once you have her controlled in the arena at all three gaits and can stop, turn and back her, then it is time to introduce another horse.
You will do the same exercises with the other horse in the arena, but sometimes you will be going in the same direction, sometimes you won't. Keep her moving and listening only to you. If she starts getting stressed, try circles and leg yields and some backing.
Only once she can safely be ridden around other horses in the arena can you take her back out on the trails.