Stop insulting mules.
Mules are lovely animals and, while it’s true that they typically don’t enjoy drilling things they already know well, they don’t “hate” arena work. Because the majority of mule owners use their mules just for trail riding, most mules don’t spend much/any time in arenas, but those that are trained in arenas work perfectly well there.
You say:
She is constantly sluggish and has zero will to work or please. In the arena, it is difficult for her to have a consistent, rhythmic trot, and it is very difficult to push her into the canter, and when you do it is quite unbalanced and she is constantly trying to break back into the trot
and
She’s sluggish in all arenas, except grass ones that make her “feel” like she’s outside.
I don’t think those behaviors indicate that your horse hates arena work. Rather, they indicate that there is something about arena work, especially in sand/dirt arenas, that is making her uncomfortable. Lack of soundness, lack of fitness…something (or some things).
Will your horse trot and canter well in smaller, arena-size circles out in an open grass field? Is the horse better working in large arenas, as opposed to a dressage arena? If the answers are no the the first question and yes to the second, than you’ve almost certainly got some kind of specific soundness, fitness, and/or training issue and not some general “I hate arenas” problem.
If you’re absolutely certain that there are no soundness issues, then I would stay out of arenas for a while and work on trails and in large open areas. Focus on building fitness, increasing responsiveness to the leg, and maintaining pace. Then work on bending and making balanced circles using natural obstacles, like circles around big trees or circles around jumps out in the field, all while maintaining pace.
The trainer that started my mule under saddle and did some remedial work with my current horse after I bought him was a big fan of riding square circles out in a big open grass field as a training tool.
Then, gradually add arena work. Very short doses to start with and building up over time.