I'll echo the need for you to dump your current trainer, and find one with YOUR interests, not HERS in mind. Keep in mind that the sooner you start showing, the sooner she will start making more money off of you. A good trainer should be more concerned about what you want- they will help you towards your goal of showing, but they won't push you towards it when you shouldn't be pushed. And they DEFINITELY won't put you on horses that are a danger to you. There's a line between pushing you out of your comfort zone to build your confidence and have you test yourself and being inconsiderate and dangerous, and she has obviously crossed that. I'm sure as a horse person you and your trainer understand that falls happen, but that doesn't mean that you should tempt fate with horses that you aren't ready for in a discipline and saddle that is completely foreign to you.
What I think that you need to do is find yourself a new barn and a new instructor. In your search visit all of the options in your area that meet your criteria- price, distance, discipline, etc. Talk to all of the possible trainers, visit the facility and horses, talk to the trainer's current students, and even see if you can watch a bit of a lesson. You'll be able to see what you like and what you don't like, weigh your options, and pick a place. If that one doesn't work out, try out your second choice. Of course, this only really works if there are multiple options around you. It's kind of slim pickings around here unfortunately