Hm. Sort of sounds like my mare, when she has figured out that her rider is inexperienced. She will "bulge out" in an attempt to ignore leg cues. She only does this when the rider gives a leg cue, and always does it on the side where the leg cue is applied. She ends up becoming very crooked, almost like someone is over-bending her to one side causing her to walk forwards very crookedly.
Straightness is actually a very important part of learning to ride. I'd even go far as to say that straightness is one of the most fundamental basics, but is probably the most overlooked aspect, and is probably even the most difficult to master.
Developing straightness can fix so many problems riders have with their horses under saddle because the whole idea puts your horse "between your legs", right where they need to be to listen and perform. Because any time your horse is not soft to the bridle, seat, AND legs, is a time when your horse is not 100% listening. If your horse isn't straight, they are not truly "there" and ready to work.
But to develop straightness, you will need an instructor or experienced rider with a good eye who can tell/show you how. So many people online and through word-of-mouth had tried to explain the concepts to me for years, but I never quite got it until I had one lesson with an experienced instructor.
I do think your horse is avoiding work.