You are riding your horse around the arena on the left rein and it seems that your horse always wants to carry his head to the outside (right) when travelling in this direction. You end up with a sore left arm from trying to hold the horse on line to the left. On left turns he falls in badly and when you ask for trot you end up with his head in your face!
Your horse is typically laterally and longitudinally unbalanced. This means he carries too much weight on the left side and too much weight on the forehand. This means that he will be over burdening his left front leg, which manifests itself in the heavy contact on the left rein. As the left front leg is being over burdened the right hind is escaping to the right in an attempt to balance the load. This is not caused by the rider - but can be compounded by it—it is the horse’s inherent natural crookedness, which may be fine for day-to-day mooching out on the range, but does not make for a comfortable ride for horse or rider. We have to adjust the horses balance to an ‘acquired straightness’ that makes the load easier for it to carry. This will prevent the horse from prematurely breaking down.
The faults aren’t only that the left front is carrying too much weight and the right hind is escaping to the right; the left hind is not stepping forward underneath the load enough. This means the hind legs are moving in two different directions and the short-stepping left hind adds to the weight in the left rein.
There’s more going wrong too; as the legs are moving in slightly different directions, the horse's hips are positioned at an angle. The right hip is more forward (and to the right) than the left hip. This also affects the position of the shoulders as the shoulder drifts to the left and is the cause of that falling in on the left rein. The horse will drift out on right turns and may be extremely difficult to even turn right.
You may recognise this next description if it applies in your own riding. The above listed faults will result in a more or less pronounced, permanent lowering of the right side of the horse’s back. It shows itself in the rider’s position in that she is now sitting on a slope. The right seat bone has a lower support base than the left. If the rider is right handed and therefore more uncoordinated on the left side, she is unable to stretch the left leg down in order to bend the left hind leg and keep her pelvis level. Instead, she will slide "down the slope" that the horse's back is providing. To prevent herself from falling off to the right side, the rider will now compensate for this unlevel support base by inclining her shoulders over to the left, amounting to the common collapsed left hip.
You can see why, now, that riding is not about a pretty head position and a good trainer will always begin by addressing the issue of straightness over poor head carriage. A good trainer will assess the horse from back to front and this is why you may not see the horse working in a good outline right away. They are feeling the horse for its imbalances and where he needs the work; not just imposing a wrong, for his stage of training and development, ‘frame’ on him. The poor head carriage is a symptom, the crookedness is the cause and as such will it be dealt with methodically over time for a full recovery rather than just applying a sticking plaster over the head carriage.
So, to begin, you have to gain control over the hind legs. The right hind has to be brought back under the body and the left leg encouraged to step further forward. As you use your left calf, the horse may try to speed up to avoid placing the leg further forward and carrying more load. Be prepared for careful use of the half halt to control the tempo If speeding up fails, he may try to push the hindquarters out to the right. Catch this with your outside calf and redirect the right hind back under the body. The horse may also try to push his shoulders to the left. You have to catch this with your left knee and thigh and by supporting the base of the neck, by the withers, with the left rein. You may need to take a little more weight into the right seat bone and stirrup to help counteract these evasions.
Once the lateral balance improves so will the longitudinal. Your horse will be much less on the forehand which will also improve the quality of the transitions. The horse can only invert if one or both hind legs go out behind you. If you drive the inside hind leg underneath you and bend it underneath your weight, the horse will not only flex the hind leg, he will also tuck his pelvis, lift his back, raise his withers, and arch his neck with a relaxed poll.
This all presupposes that you as a rider have the necessary tools in your riding kit box to deal with all these fluctuations. At times it can demand a strong seat and leg aids to prevent you simply being pushed out of the way by the horse.
To help develop a strong—effective, not forceful—seat check out these other pages:
Part Two - How to Straighten the Horse
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Classical Dressage Notebook