I agree with BarrelracingArabian. I would not let her push you around. You say she is respecting you but she is not. She still lets you know and bullies you into not touching her or cinching her up. You have to realize that she will bite you, she just hasn't had to yet because you have backed off. And she won't feel bad either.
Have someone stand at her head when cinching or brushing. If she even flinches, you need to discipline her. Use a rope halter and get her attention. I can tell you that eventually she will bite you and will continue to bully you. And riding with a loose saddle is extremely dangerous, just because you don't want to upset her and tighten the cinch.