I think I get it now.
Her standing martingales are really, REALLY loose. As a safety precaution to make sure the horse doesn't throw his head into your face. They can still jump with it and not be pulled back. The reason she was recommending I go back to it was that she WAS throwing her head in my face and feeling less confined without it so running around the ring. I, personally, don't believe in martingales for this purpose, but to each his own.
The gag bits are NOT on every horse. The gag bits are on the green horses with advanced riders that know how to handle them and not to go pulling hard on the bottom rein all the time. Maybe even at all.
The ACE thing...I can't defend that. After minor research, she's being really, REALLY stupid. No matter how low the dose, the Ace impairs learning and is also generally a bad practice if one is riding. I will NEVER willingly do this. Ever.
I think I understand some of the things she's doing now that most riders disapprove of and I'm going to keep riding with her. I love her instruction and I improve riding drastically each year. I know now what she's been doing wrong and I'll keep it in mind so that when I have horses of my own I don't do it.
Thanks for all your help, guys. :)