Welcome to the confusing world of gaited horses. Been there done that. We had the same problem when we switched to gaited horses. The folks that know how, will seldom tell you, because of the arguments they get. When we finally found someone that would share their info, many of our gaiting problems went away. Quite simply put, you don't ride gaited horses like trotting horses. Yes, you'll hear those that say you can, but, that's only the case in a very small percentage of us. We ride with a lot of gaited horses and the majority of the problems gaited riders have is related to the way they ride. They are trying to ride them like trotting horses. For most of us, that simply will not work. If you ride them like a trotting horse, you are teaching them to trot or pace.
This gets even more confusing when we don't know what gait the horse has as it's signature gait, and/or the signature gait of the horse is a trot. Just because they have the name of gaited horse doesn't mean their signature gait is gaited.
If your horse is gaiting and then "switches gears" to something that is not smooth, it is probably something with the way it is being ridden. That is a good example of teaching a horse to trot with the way it is being ridden, ie, the horse is probably naturally gaited, and it starts off gaiting, then the way it is ridden tells it to do something different, like trot.
I'm one of those small percentages that do not follow the old gaited horse world of myths on riding, training, and equipment.
A rider needs to be balanced period in order to gait (either gaited or non gaited)
I have found that if you ride in a forward seat tends to bring out a trot or pace, again I suggest a balanced seat, not forward, not on pockets.
Lee Ziegler, Larry Whitesell, Beverly (shoot forgot her last name LOL)and Diane Gueck are some good examples to look up.
Gaited horses are very awesome to ride once you become a balanced rider;)