It all depends on eventually what your daughter would like to persue. I would personally go with the dressage or western lessons. Scrap the english lessons unless it's with a good coach that will help her learn to ride properly, and teach her good horsemanship basics on the ground without compromising her safety.
In my experience as a rider starting out at a young age (I started riding at 7 with no prior horsey experience) with english coaches, I have spent most of my riding career after riding with these "trainers" building up my confidence again, re-learning how to do things and eliminating bad habits. It is only with english trainers that I have been pushed too far too fast, been put on unsafe and unsuitable horses and been taught things blatantly wrong. I had a short stint of reining lessons with a western coach and they were amazing, I've also been to cattle penning clinics and ridden at various western barns, all with wonderful instruction and safe horse practices.
Also in my experience with dressage instructors, even the ones that are "awful" they are still better than most of the "good" english trainers. They aren't about to throw your kid on a green broke TB, and they are going to make sure your daughter learns proper equitation before chucking her over 3' fences.