RE: your horse falling on her forehand (falling foward when she stops)--ALL horses are made with 4 legs, BUT they naturally carry more weight on their front 2 legs than one their back 2 legs. It must be that big 'ole head and neck! Ha, ha When you add weight, then they will carry you AND their head and neck on their front 2 legs. For example, a 900 pound horse starts with 600 pound on the front legs and 300 pounds on the back legs, PLUS your ~150 pounds=750 pounds on the front 2 legs and the leftover 300 pounds on the back 2 legs. They KNOW how to shift their own weight backwards when it matters to them, but they're lazy...like we were in gym class. Collection corrects this. Collection comes with hard work and it takes time. There is no need to apologize for what you don't know, or what your horse doesn't know. It's great that you have a coach as a good resource, and that will help you a lot! **hugs**
Sometimes I HATE the InterWEB!!!! I had some trouble finding more than one Good video for you, but I'll give you a short caveat before you watch this one. (Maybe someone else here has some more bookmarked.) Watch the rider tighten her lower back muscles and her butt--this is what YOU will practice, along with sqeezing your lower leg and stop following the bit. Ignore lateral rein talk, etc.--THIS is confusing until this vocabulary becomes part of your own vocabulary. K.I.S.S. And just stop following the horse to stop HIS movement. If you practice just THAT, the rest will make sense. I agree with ALL of the other stuff they talk about. The Horse | How to Do a Half Halt (video)
BTW, sitting deep is best learned in MHO by riding long, long periods and learning to sit heavy in the saddle by becoming a tired and Relaxed rider. Otherwise I don't believe that sitting deep can be taught if you only ride an hour at a time. Many of my riding students (1985-1994) could still push themselves out of the saddle after an hour lesson, even when I worked them hard by doing things like posting without stirrups.
I'm sure that mastering the half-halt will really help your riding and really get your horse to listen to you. EVERY riding discipline uses it, even if they might have another word for it. LOL