My son Brennen's yearling Appy colt Freddie started doing something similar, although he hasn't been invading Brennen's space. Often, when Brennen ask Freddie to lope, he'll turn and double barrel.
He never comes close to anybody, but we have figured out that his instructor getting him to bring Freddie down when in the wrong lead have scared him a bit.
Brennen uses a chain on him when lunging and has a lot of control otherwise. Our plan is to finish building our round pen, then free lunge him so that he can get comfortable loping on command again.