Here are a couple of things I did with Mia:
1 - The Cones of Confusion. 3 cones, set far enough apart that I could do a very tight figure 8 between any two. I'd enter the CoC between two cones, and then decide if I wanted to go left, right, or around the far cone. This prevented Mia from knowing in advance what I wanted, since I didn't know myself. It forced her to wait for my cues. I also kept the option of blowing straight thru the CoC, or circling around them on the outside for variety.
2 - I set 2 cones further apart than with the CoC. Perpendicular to the line between them, and extending out 70-80 feet, another cone, forming a tall isosceles triangle. We could do a figure 8, or just go around one cone, and then head back to the far cone. That way, she would do a turn or two at the most before getting a straight line. We could walk the double cones and then trot to the far one, etc. We could also canter a loop around all of the cones. That kept us from doing the same thing over and over again.
she is definitely not confused
I know which direction she wants to go
Back towards the house
If I decide to turn her in the direction she wants to go -- no problem at all
Makes me think she is
being naughty. That isn't confusion or not being physically capable of turning. It is defiance - "You're not the boss of me!" Mia only does that once in a great while, and never for very long, so I cannot give a lot of tested advice.
However, what the trainer had me do when she was working with both of us was work her in a round pen from the ground. Nothing complex, but W/T/C, turns outside and inside, going the pace I wanted & the distance I wanted. The first few times, Mia did a lot of kicking in the air and galloping when told to walk or trot.
In the saddle, I've been very aggressive with her if she tries to turn the wrong way or against my wishes. That goes back to her "pre-curb bit" days, when she would fight a snaffle or rope sidepull halter. She got to choose how much pressure was applied. If she turned her head to the left when asked with a pinkie, that was great. If it took my shoulder and back...that was OK too. Her choice. I'd ask with an opening rein. Pressure escalated from there. On a couple of occasions, when I needed to turn us immediately on a trail to prevent us from hitting something very nasty or going off a small ledge, then 'tear her face off
' might describe my reaction. Just as a horse may decide it can accept your kicking as preferable to going faster, it can accept small tugs or leg pressure and ignore them.
Without seeing what is going on, it is hard to give good advice. How does your trainer handle it when she refuses to go the right direction for her?