Hi apache. Its sunday am here, so a lot of folks are out riding, so no answer on the forum. I am here, tho.
I think I have an idea of what you are talking about. In barrel racing the horse has to turn so fast that sometimes they whip around the barrel actually counter bent. I guess better to say , they move very boardlike, like a gate swinging on a hinge, and their inside shoulder drops down really close to the barrel and they kind of "fall" toward it while they scramble around the outside and then run off.
So, your horse only knows how to turn by falling into the middle and spinning around, the "short turn " you were talking about
To teach him how to turn in an even arc you will need to get him softer to the bit and knowing how to "follow" the bit to the inside when he turns. That is, you ask for inside bend, he flexes his inside jaw such that you can see his eye, and he steps around in a mild arc, keeping his inside shoulder up .
I will post more in a minute.