Most people who own Aus. Stock horses in australia probably wouldn't even know what a lateral movement was if I asked them lol. What characteristics would a horse need to have to be able to be taught these movements.
Wow, so that's super offensive to someone who owns ASH in Australia...
True, most people who own ASh don't ride a lot of *competitive* dressage. But working stock horses sure as hell need to know how to move off leg, be light on the aids, have a good solid stop, good solid, straight back up and have a cool mind. The majority of *reputable* breeders and resellers will also have a solid flying change on their horses.
If you want to be successful in ASh classes, your horse will ALSO need to show decent collection. So you must not be looking in the right places if you are finding horses and owners ignorant of any of these concepts. If you don't mind me asking, what is your budget? Have a look on breeders websites and get a feelf or the market and quality of horses. There are quite a few nice ASH in this months horse deals, which you can view online.