It sounds like he doesn't know what he doing when you are asking him to go around the barrel. It hasn't "clicked" in his mind yet to turn around it. But I would get a really good foundation under him before putting the pattern infront of him. It takes time, it could take a month or more to have a super responsive horse under saddle. And even that is with daily riding and someone who knows how to train a horse really well.
Do you have cones that you could set up? I would set those in a square pattern, one in each corner and go. I drew a really horrible picture that I'll attach so you can kind of see what I'm taking about. Just turn around those cones but down make it obvious what your going to do. Turn different directions. Instead of going in the same direction (clockwise) go counterclockwise, or cut through diagonally. Be creative and make it fun for him.
You can also do this without cones. Just walk around and randomly turn. But dont ask him to turn ontop of himself, just a nice wide turn will do until he gets the hang of it, then you can start asking him to turn tighter and tighter around himself.
"The greatest pleasure of a dog is that you may make a fool of yourself with
him and not only will he not scold you, but he will make a fool of himself too."