Absolutely teach this horse to turn to the right. FIX the problem -- not avoid it.
If I am near the ranch and not 10 miles away in a pasture or on a trail, I will just take the horse to the round pen and check the right rein 'lightly' to the back girth on the right side using a full cheek snaffle. I use a ring of rubber cut out of an old inner-tube to actually tie the rein to so it can 'give'. Then, I let the horse go around the round-pen loose. I let it stay on the rail until it goes around at a trot with its head giving to that right rein and keeping it to the inside. Then, I start stepping in front of the horse and teaching it to make a small 360 degree right circle every time I do. This softens up a horse so well for teaching it to 'follow its nose', that I do this with every horse, both directions, before I ride it and any time after that when it is not listening. I do this instead of longing or 'working a horse down' any other way.
Now, if I am out in the pasture moving or checking cattle and the horse refuses to turn to the right, I start working on those right ribs with my inside leg. If you 'soften' up those ribs and get the horse to push them out to the left, the tug-o-war is over. If you only work on the right rein, you stand a chance of forcing the horse to rear. If you work on those right ribs and hips, you get the solution without as much confrontation. Once the horse will disengage it hips to the left and will push its ribs out, it will start giving you its head because you are taken the power away from it that it was stiffening its body with.
If you keep a horse going forward (but not real fast), keep its head as much as possible to the right and keep working over those ribs on the right, it will finally give in and give you its head and follow its nose to the right.
Letting it fight itself in the round pen is sure easier and more productive. A horse that I have taught to follow its nose this way in the round pen has NEVER gone stiff to me on one side or the other. Horses I have had to fight it out with in a pasture have all been someone else's horse that had refused to turn for them.