She's adorable, and looks like a blast to ride. I'm glad that you have decided to take off the martingale, since I think that a lot of your problems are stemming from her kind of bracing against it. Maybe you guys were just having a bad day, since she looks super excited in these, yet in the others ones you posted she looks much quieter. In these pictures you really need to look up. If your horse acts up, don't look down at it, that isn't going to help anything. Always look up to where you are going. In a lot of the pictures you also seem to be bracing against your stirrups and against her mouth. Move your leg back, and try to use more seat to control her then hand. And relax! You look so tense and nervous! Remember, horses can feel that and feed off of it!.
Also, this is kind of a pet peeve of mine.. you are thinking about starting to teach her dressage? If a horse is jumping, they should know basics in dressage. They should be able to do a shoulder in, haunches in, etc. They should be able to extend and collect. All of this will help you in jumping. If a horse has a solid foundation in flatwork it is much more beneficial to them, especially when you start jumping.