Lateral work is most beneficial when the horse stays relaxed in its body. It is not generally a good idea to "push through" a movement with tension present. It's a much better idea to come out of it, circle, improve your connection, and start again.
“You need to produce a walk. So work at the walk as well as the trot and canter. Get a good feeling of the body working in the walk. The walk is a mirror of the training of the horse.” ~ Christoph Hess
In the sport of Eventing, ensuring that our horses are truly fit for our level of competition is one of the best ways to prevent unnecessary injuries.
When riding Dressage, we want our horses to reach and push forward through the neck into the rein connection. This happens as a result of the horse's back engaging and lifting... similar to a nice round bascule over a jump.
Horses become incapable of learning when they go past a certain level of fear, anxiety, or stress. This means that if you keep hammering away at the horse, trying to teach them something when they are currently overwhelmed with stress, it will not work.