I would assume for barrel racing, a nice tight turn is good. To practice turning, at the walk, even just while you are warming up, do frequent 180 degree changes of direction, but make the horse turn off his hind end, not pulling him around with the reins. Turning on the hind end involves using your legs correctly. Just play with it until you find a leg placement that your horse will respond to and turn around smoothly and compact. It'll probably be inside leg slightly behind the girth and outside leg at the girth to keep him from bulging out his shoulder, but just remember the goal is to turn with your body, not reins. Just google turn on the haunches and rollback turns.
For building muscle, it's as simple as going out into the woods or hilly fields and walking the horse up and down hills in a nice forward marching walk. Not gigantic hills, just enough slope to make if varied terrain.
You just have to see your distance...you don't have to like it.