Why has the family feud lasted three generations, and why don't Ulrich and Georg just shoot each other?
The family feud lasted three generations because the von Gradwitz and Znaeym families preserved mutual hostilities long after the original feuding parties passed away. The text tells us that the conflict began in the days of Ulrich von Gradwitz's grandfather. Then, a lawsuit had been brought against "a neighboring family of petty landowners" (presumably Georg Znaeym's family).
By all indications, the Znaeym family had never "acquiesced in the judgment of the Courts, and a long series of poaching affrays and similar scandals... embittered the relationships between the families for three generations." So, the younger members of each family have essentially inherited the original quarrel between the forefathers.
In the present, Ulrich views Georg as "the inheritor of the quarrel and the tireless game-snatcher and raider of the disputed border-forest." The men are energized by their mutual hatred for each other; each intends to kill the other, should the opportunity present itself.
One night, Ulrich does come face to face with his enemy. However, he finds it difficult to shoot down his enemy in cold blood.
But a man who has been brought up under the code of a restraining civilization cannot easily nerve himself to shoot down his neighbor in cold blood and without word spoken, except for an offense against his hearth and honor.
The irony of the situation is that Ulrich cannot overcome a lifetime of genteel habits to exact his immediate revenge upon Georg. He feels compelled to afford him the formality of an explanation, despite his disinclination to speak civilly to his mortal enemy. Ulrich's internal conflict is between his dormant sense of decency and his consuming, visceral hatred of Georg. Because of his hesitation, Ulrich is ultimately prevented from accomplishing his original goal, which is to kill Georg.
Just at the moment of hesitation, the furious storm unleashes strong winds that bring down a gigantic beech tree upon the two men. Both Georg and Ulrich end up being pinned down tightly by the massive branches of the tree. By now, all thoughts of shooting each other have been banished from their minds. They find themselves immobilized and helpless; their only thought is of self-preservation and survival. Later, both men declare a truce of sorts with each other. However, the story ends on an ominous note. With the approach of wolves, we are led to wonder whether both men will die side by side or be rescued in the nick of time by their servants.
The feud between the Gradwitz family and the Znaeym family has continued for three generations because the Znaeym family has never recognized the Court's judgment to remove them from the Gradwitz land. The Znaeym family has continued to hunt and otherwise trespass on the land. In the current generation, the feud has become more personal and potentially violent.
Ulrich and Georg do not shoot each other when they meet for a few reasons. First, they meet face to face and probably do not have enough time and/or distance to raise a weapon without the thwarting the attempt or mirroring it. Also, both men have been raised to be courteous, even if not warmly; manners prevent one man from harming another after meeting in such close proximity. Finally, before either can act, a tree pins both of them to the ground, giving no time for personal interaction before trapping them.