I certainly hope that the improvements continue, and that you are able to take a spoonful of cement and just get on with it rather than feeling like a victim. You created the problem, now you ned to fix it. It's time to buck up and own it.
As others have said, this is not a dressage vs any other discipline issue. I am a Dressage rider, and I'll be ****ed if I allowed any horse in my care to behave the way yours does. Even my now rising 3 year old, who is cheeky as all heck and very much needs breaking in before he turns into some kind of destructor tornado, wouldn't DARE put a hoof on him. If he so much as puts his ears back at me, he thinks twice and sharpens up super quickly.
A half tonne animal that comes equipped with solid muscle, a huge amount of power, hard hooves and sharp teeth cannot be given an inch when it comes to respect. They are not cute little play things, they can and do kill and seriously injure people on a daily basis. My own coach with 40 years experience and an accomplished FEI dressage rider, breaker and trainer, was kicked just above the knee once. Not even a hard kick, and she ended up with two knee caps and a femur almost poking through her skin. Not her own horse mind you!
Don't even think about Dressage training right now. If you can't get respect on the ground, do you seriously expect this mare to respect you while you're on her back, telling her to work for you? Good luck with that.
Get the ground work down pat, expect her to be a meek little lamb before you get on. Give her 'the eye' and she should back right off immediately.