Lateral work is the bread and butter for my instuctor. We've done a lot of different things over the years to work on the different issues as our training slowly comes along.
It is very interesting to see that we do or did quite a few of the things already mentioned above.
My horse is on the heavier side. He's a Welsh Cob, "energy efficient", not really a pleaser. We had huge issues with straighness and forward. He loves to just plow through life with and on his massive shoulders and tends to forget that he actually has the massive haunches to go with those...
He also lives in constant fear of falling on his face when asked to use BOTH his hind legs evenly. This is especially apparent in the halt and during travers to the right, with his weaker hind leg leading.
When we first started we did a lot of SI/HI/renvers/travers along the rail sometimes through the corners on straight lines. We never did LY.
Once the basics were working we started to do a lot of changes in the lateral work. SI to HI every few steps by realigning the shoulders to the haunches (and not the other way around). The idea was to really get his shoulders up and under control and in front of his haunches.
We also did the walk/halt, trot/halt in alignment Mountaineer mentioned. Only we stayed on the rail for those. My instuctor still belives that we will get Crispin to piaffe one day and especially the trot/halt in SI helped to get more "sit" into his hind end.
Like I said above, he also lives in constant fear of falling on his face. So step by step and stop and go it is in travers for him too. Otherwise he tends to rush through them. Generally, we do most of our lateral work s-l-o-w. Crispin likes to not listen and rush through the harder parts.
We introduced CC and it became apparent that c/w transitions needed work. This is where HI on a circle comes in (10m). The haunches doing a smaller circle is helping him carry more with his hind end (we are also doing those circles counter bend at the trot for the same reason).
And then there are those exercises that aren't really "dressage movements" but are also helping a lot. For example, we do a little excercise we call the cross. It's halt, full pass left, halt, full pass right, halt, rb, halt, forward, halt, rb. Slowly, step by step. Only 2-4 steps each. It hepls with reactivity, mobility and listening to the aids.
We also something we call the clock. On the haunches or on the forhand we turn around and obstacle like the hand of a clock. We usually use the mounting block. The obstacle helps to keep position and have, again, a little more "sit" in the haunches.
When by myself I like SI to travers to SI. And something my instuctor calls "passade". It's not quite that. it's travers from the rail to the center line, a turn on the forhand in travers (or HI) and travers back to the rail.
This is from our first ride trying the passade. I can see all our little issues, how uneven he is behind, rushing to get his "good" leg under and get me out of the way in the prosess.
https://youtu.be/PDElGBHTbQA