"My gf has been dying to take dressage lessons with her TWH. She finally has an instructor come to the house. The instructor tells her she can't work with a gaited horse."
PrincessFluffyBreeches, I am so sorry that your friend experienced this feedback from a traditional dressage instructor. I've bumped into this attitude a couple of times, but most dressage instructors I've encountered have been very encouraging. I would find a new dressage instructor, because dressage is more than trot. Dressage training helps all breeds of horses whether they trot or gait.
If your goal is to improve balance, relaxation, suppleness, engagement, harmony, and rider position, then dressage training is a great way to go.
If your goal is to show at United States Dressage Federation USDF shows, it is required that your horse trots.
But there are USDF schooling dressage shows that are open to gaited dressage using National Walking Horse Association NWHA gaited dressage tests and Friends of Sound Horses FOSH gaited dressage tests. Just ask the schooling show manager if you can use these tests to ride your gaited dressage horse.
I've been applying dressage methods of training with my TWH for 7 years and it has helped develop my horses gaits. And I've shown at dozens of USDF schooling shows using gaited dressage tests. So tell you friend if she is interested in dressage for her gaited horse, don't give up! :)