I don't want to step on toes but I disagree with your trainer.
One of my trainers also does both dressage and hunter jumpers but you do not show your chest where you are going, that creates crookedness. Looking too far to the inside creates crookedness, where as looking to the outside tends to help correct the crookedness that creates. The idea isn't that you're constantly leaning one way or the other but that you find straight and center, so you can then see how you move your body affects the horse. If your always crooked the horse will adapt to compensate.
Horses definitely travel in the direction where you put your weight. It's like if I put a 20lb backpack on you and you had it swung over one shoulder you're naturally inclined to follow the weight of the backpack. And I can say from breaking babies that is how we teach them to steer or if you ride a school master that is how they steer. It's based off of where you put your weight. Like if your rode my young horse and didn't steer that way he would have no problem running you into the wall because he puts himself under your weight. He's also a horse who can contort and twist his body in a variety of ways, so if you're not pretty straight and aware of all his pieces he will contort himself like a zig-zag (arabs are known for this). If you want him to leg yield, you almost just position, step into the outside stirrup, look where you're going and ask. The steepness being controlled between the inside leg and the outside rein. Straightness off of position and organization. If you step into the inside stirrup you may need to guide him with the outside leg because I will say we teach them to follow our weight because our goal in training is that our effort appear effortless even though nobody knows how many hours we've spent training to get it to look effortless.
I say this because straightness matters in dressage ESPECIALLY when you start moving into 2nd and 3rd level when you're doing a lot of laterals and movements and counter canter, simple and flying changes. When you do half pass and you go haunches in and into half pass (same with piroettes). Haunches in you sit more to your inside seat bone and lift the outside seat bone with the outside leg back, inside leg at girth to keep bend through the rib cage as the haunches are brought around the inside leg, then as you go into half pass you just ask the horse to travel side ways from the haunches in looking between the ears. What you see between the ears is where you're headed. If that makes sense.
Or when you pick up true canter inside leg at the girth, outside leg behind and I look over the outside shoulder if they're not getting true canter because it puts my seat bones where they need to be for canter, so that when I teach the horse to pick up either lead of canter I can get it based on my position if that makes sense. When you turn with the outside shoulder forward like you're looking where you're going, your outside seat bone is forward, inside seat bone back and that is not in line with the shoulders or the horse at canter. Inside shoulder should be forward, inside seat bone forward, outside seat bone back as you ask because you are in a way mimicking and following the horse's body. If that makes sense.
My youngster in shoulder in, so you can see where my shoulders are in relationship to him and how his body is responding. He's pretty straight but correctly bent around my inside leg in shoulder in. It's consistent. https://www.youtube.com/watch?v=yJswKAohbwI
Charlotte Dujardin. World number 1 dressage rider. Just note this is a very hot, strong and difficult young horse but it shows you a lot of what dressage riders do. There are moments when she does turn her chest in but that's for the hind leg. https://www.youtube.com/watch?v=AXpROP5ht34
I'm including other riders too who aren't world class, except for Catherine Haddad. https://www.youtube.com/watch?v=0tcB...TXddQ&index=86 https://www.youtube.com/watch?v=h8AneU8jz94 https://www.youtube.com/watch?v=nLM_1MXjp1o
Sorry went really long with this but I'm trying to explain and I'm not always good at that so I get long winded trying to be detailed and conclusive. But I was going to say to your understanding of basics will constantly evolve as you discover better and better ways to do things. This is constant you'll always evolve and learn as you progress. All this sport is is learning new and better ways to do something. The moment you start feeling like you know what you're doing and you got this, you will ride a horse who will teach you a whole new set of rules and ways to ride. I think it's what makes it so hard to get cocky because every time you start feeling like you know your stuff and youre awesome, you will get knocked down many pegs and sometimes in the dirt. It's wonderful lol.