It is only natural for horses in a group ride to be anxious about the speed. No one wants to be left behind, and if the TWH was gaiting in front of your horse, and the Arab jigging, that only transmits that nervous energy to your horse.
Constantly riding with the brake on is just going to irritate the both of you and wear out your brakes. You want to retune your brakes with some work in the arena, before goin out on the trail.
You want to go forward at a walk, apply the reins with one rein tighter than the other. Apply gradually , increasing the pressure to a dead stop of your hands if the horse won't stop. You become concrete, in your hands and in your body. Pick a spot on the ground. When you are about one horse length or a tad more from that spot (approaching it at a walk) begin asking for a halt, increase, increase gradually and when you reach the place where YOUR hands go over that spot, you anchor them to the ground, and your body, and you just STOP riding . The horse will feel that total rigidity in your body. YOU don't move your hands until he comes to a complete halt AND backs off the bit one step . He will eventually get to almost bouncing off the bit. But it is important that you stop your body and become like concrete and get the horse to come off the bit and step backward. The second she does, give her 6 inches of rein and praise. If she steps forward, concrete your hands and ask for that bounce off the bit and step back a;nd you release.
Once you have the hrose light to the halt, then when you trail ride, bring her to a halt, back up one or two steps and then ask her to "walk".
Also, it's important on a trail ride that no one horse must carry the lead the entire trip. YOu want to have the leader "peel off" and go to the back of the line and then "peel in" behind the last horse so there's a new leader. And on and on, every 10 minutes or so.