ha ha ! no, you stopped just fine (after half an hour of crazy running ahum).
When turning (which would be a different subject actually) stay straight in the saddle (you can feel that when you can feel both your seatbones evenly in the saddle)
Rotate your pelvis forward a bit and then turn your upper body and pelvis into the direction you want to go, looking over the ears of your horse on to the spot of ground you want to end up in a few paces.
Make sure your breathing is low and relaxed so your body stays soft and your pelvis open.
When you do this, the ribcage of the horse gets a gentle bent.
Second, your horse's balance is somewhat disturbed.
Prey animals want to keep perfect balance at all cost.
the only thing they would have to do in this case to restore balance is turn their body with the riders pelvis, after which both horse and rider's shoulders will follow a straight line again and the balance is restored.
Turning this will enhance a turn from the inner hind leg which will ensure correct bending and thus correct gymnastics.
You do not have to do anything with your legs as they will fall right into the right place.
If the horse does not oblige you can give some pressure or a light squeeze or nodge with your inside leg or outside leg (depends on which way the horse is moving, to much in or out)
If the horse does not want to turn, then you can indeed put some pressure in your inside stirrup, but that indeed can cause more inbalance and weight to the inside shoulder so use it only in small doses.
Turning by the head like most riders do these days(with the inner rein even) will of course make all balance lost as the balance key is the head of the horse.
The horse will then turn on the inside shoulder which makes the circle harmful for the body.
ps have someone on all fours and try it out (and visa versa), you'll see what I mean and see how it works
The different schools of thought on weight bearing in the turn give us great pause for thought, as it should.
I think an important consideration should be what to do determined by the speed of the turn, and of course the radius of the turn.
I've experienced problem and the solution for one of my horse "sports," in the past. The reining stock horse in western competition.
Being square in body through all turns is part of the discipline when the turns are large, and even small while following a curving track, but in two 'turns,' the rollback, and the spin, things change rather dramatically.
And how one responds in training determines how one uses their body in competition, where the turns actually are done differently.
For example, as one rides (while training) at an angle toward a fence, just as one reaches the fence (and it's time to turn) the turn cue with the rein is joined to the outside leg pressure to signal the horse to set his hindquarters, and the body makes, from the vertical, a very slight tilt to the outside hind leg.
Originally it was thought that this helped (and I hear some trainers still claim this) lock the horses leg down so he will come under with it and push off with it coming out of the rollback.
In fact, what happens that loads the hindquarters is the freeing of the forehand by that slight release of weight over the forehand.
The horse can come up, effectively collecting much the same as a horse trained in dressage does to pirouette.
The slight tipping back and away from the turn has far more to do with releasing the forehand than loading the hindquarters.
One might feel it at low speed, low energy (not much impulsion) but that would be difficult.
As the horse develops more energy in these turns it is far more easy to feel.
One can see it at its most extreme in the fast changes of direction of the cutting horse, forehand low to the ground, but being lifted, and shifted to the side.
If the rider sat strictly straight up, they would forever be crushing the horse's back and stomach that does the lifting from the fulcrum of the stifle.
And the forehand would have to be "jumped" upward by the horse to move it at all.
The rider, in cutting, and in fast reining work appears almost to be being whipped back and forth.
In my mind, as I look at the biomechanics involved and slow motion it, with multiple frozen images being trailed behind, I think of it as incremental surge.
The horse and the rider's mass is being left a bit behind, then catches up, then passes the theoretical center of mass (that would exist in the still horse and rider) then move beyond and will rebound, both if all motion stops, or if it reverses.
This is what requires a strong core for rider and horse. Flexible strength. The ability to regulate the response of a muscle or group of muscles so that they do not lock up with the movement and attempt to remain fixed in relation to the center of mass.
You know the riders when you see them. Common in beginners and sometimes sticks around when the instructor asks for good form, but can't express clearly this concept of flexible even soft strength.
The aim is to be relaxed, and out of relaxed muscles to respond more gradually and smoothly to movement, and catching up to one's self, and the horse.
I've had a student or two that nearly defeated my instruction, and were terrible stiff trying to hold the "correct form."
Thus I incorporation horseback gymnastics as a way to relax and loosen them.
Easy with children, but more difficult with adults. Some adults, particularly men (both my problem students were men) are too inhibited at first to loosen up and flop about on the horse.
Eventually, with classroom work, and a lot of fun stuff to do they made it, but my goodness it took a long time.
Who would think that a major factor in good training, and conditioning, and in teaching, would be developing a sense of humor in the student rider.
Oddly enough, the horses seem to like it too. You'd think all the displacement of weight would annoy them, or frighten them, but it doesn't. Especially if people are having fun.