Chair seat is putting your weight over weakest area of back, and is unsightly and unnecessary as well. And makes it harder for horse to use themselves while saving energy.
And are you sure she is TWH, or could she be ASB? Or mix?
At any rate.
When asking for trot, bring your calves on side, at same time as you bring hands up and close together. Using this will tell horse what you are wanting.
For rack cue, open legs off sides and bring hands down and wide apart.
It may be what you are thinking is a rack, is actually a running walk too.
And never shake a horse's head in curb bit for that matter. And even snaffle may not be enough cue if horse is hard to get into gait.
But the boots/studs are messing your horse up more than likely.
Best to get your gaits done in arena or open field where you don't have to use those.
Horses make me a better person.