Lots of interesting replies on here; hope some of them are helpful. As for me, well, I've never read Lyons et al and most of what I know I've learned for myself the hard way. Since I don't know you or your horse and have never seen you ride or her carry a rider, maybe nothing I say on here is gonna be helpful, but maybe a sentence here or there will set you to thinking and ultimately that will be productive.
The thing about horses is that they are not born kind. They learn kindness over the years the same way we riders learn humility. It sounds to me like you and Lucy are at different spots in your learning--like maybe she is in 3rd grade and you're still in 2nd, so she's being snotty and superior with you the way kids can be with one another.
Your questions about bits makes me wonder if Lucy's wolf teeth are part of the problem. If the bits connect with those teeth that can be uncomfortable and even painful. Next it is important to remember that the greener the rider, the milder the bit should be. It takes an extremely well-educated hand to use a severe bit. Besides, a stock horse shouldn't be worked off the bit. He needs to be cued off his rear end because that is where everything really starts--stops, changes in lead or direction, speeding up and slowing down--all this starts from the back end. You do this with your back, seat, and legs. Your hands are just to steady him. But most beginners ride the head because they are insecure and this gives a false sense control.
To ride the whole horse and not just the head takes what I call intuitive riding. That just means you and the horse become a single unit, blending into one another until it is hard to tell where you stop and he begins. Think of yourself as a chocolate bar who melts onto the horse. Then you ride with your back, seat, and legs instead of your hands. The horse, who is so sensitive he can feel a fly on his back, senses every shift in your weight and balance and that helps him know where you are going and what you want him to do next.
For example, to stop you don't pull back on the reins. Instead you take a hold of his sides with both legs and lighten your weight on his back. Want instead to go faster? Push with your seat.
For now instead of riding Lucy, ride your old, wind-broke 22-year-old and let him teach you. You should be able to feel his movements through your seat. Practice until you can FEEL which of his feet are doing what, what lead you are in, when to cue a rollback or a spin so that he can respond most efficiently. Then you will be able to ride across a pasture and change your direction simply by looking towards the new direction. He will feel your changes in balance and will head off in the new direction. Practice stops, turns, changes in gaits and speeds by using your seat and legs. Stay off that bit and don't lean on those reins. They are there to help HIM with his balance not you with yours
I have a hunch that if your husband is using Lucy to do ranch work, he's already riding her this way...and she likes it. And like a 3rd grader she is being snotty with you because you can't ride that way yet. But once you teach yourself to ride intuitively, I am betting you will be able to ride Lucy.
And once you start riding Lucy, I think you are going to have to accept that this is an intelligent critter who gets bored easily. If you want to do arena work, you are gonna have to find ways to make it interesting and challenging for her. Her obnoxious behavior is as much about boredom as control. She wants to work and I think you have to find ways to make that need work FOR you. Right now its working against you. You're gonna have to out-think her.
Like I said, I don't know either of you, so I may be a thousand miles off base. In that case, please accept my apologies because I am really not trying to put you down or anything like that. I'm just trying to offer a different take on this.
Hope it is helpful.
Rusty