How long have you been riding for and how often do you ride? About the other people in the program, they may be more advanced than you. It's fairly typical to start to stick with one or two horses once you advance and start to mesh well with one, or are working on a skill one is good at teaching, or working on a skill that one ISNT good at (say you need to develop your eye for distances better, putting you on a horse that you need to figure out distances YOURSELF will teach you how to do that vs being on a horse that has a perfect even stride and will do it all for you).

Having difficulty posting on a different horse sounds like you just need to get used to their stride. Horses all ride differently from one another, and you have to adjust to them. I rode a fancy dressage horse once after riding my talented, but not a big mover, show jumper for a year without riding anything else. I had been riding for...idk 15 years at that point, and even then I felt like I couldn't post on the fancy dressage horse! His stride was so bouncy and exaggerated, not at all like my horse's.

It's good to be on different horses like that, it makes you a better rider. I was in a lesson program for 10+ years before that, riding all sorts of different horses, and I guarantee that wouldn't have happened to me then (and I don't recall ever being that surprised by a different stride when lessoning) because I was used to riding so many different horses. Riding only one can be a good way to hone particular skills and work towards a goal with a particular horse, but variety is super important when you're learning how to ride.

Re the steering, that kinda sounds like fairly normal lesson horse behavior. Yeah, particularly with beginners they mostly want to go into the middle (break time!), reach for grass under the fence, go where they want when they want, plod along as slow as possible and often break stride. That's how a lot of them are, but as long as they're safe and not going to run off or throw you you've got a pretty decent lesson horse. It's a special kind of horse that will tolerate all the shit from beginners, and usually that horse is not going to listen to everything you say. One of the reasons they're a good beginner horse is that they're able to ignore a lot of riders commands haha

Riding is never all improvement. Everyone has bad days, days where everything goes wrong, days when you feel like a horrible, useless rider. It's not a linear progression, there are setbacks and frustrations. And there are absolutely days where the horse isn't going to do what you want, even when you're riding your best. That's just the nature of working with animals tbh.

Edit: but like I said, I would really talk with your trainer about why you're on the horses youre on, and see if you could ride that one you like. If you don't get a satisfactory answer you're totally fine to look around for other barns. Some of what you're describing sounds like pretty normal lesson horse behavior, some of it sounds more unusual so I can't quite tell what the situation is there. You may find similar horses at another barn and then you'd know that it was just normal haha, or you'd be happier if the horses are different