Lawrence is called "Tifty" because his two brothers and his sister made up that name for him when they were small children. The sound of his slippers coming down the hall for breakfast sounded like "Tifty, tifty, tifty." But they had other names for him, including "Little Jesus" and "the Croaker." At the family reunion everybody, including his mother, still calls Lawrence "Tifty." It is not exactly a term of endearment. The name suggests that as soon as the kids heard him coming they knew he would bring bad feelings of one kind or another. He is the black sheep of the family.
The tension actually begins as soon as Tifty arrives at Laud's Island with his wife and two children. He displays a totally negative attitude throughout this family reunion. He finds fault with everything. The narrator attributes his misanthropic and pessimistic character to their ancestors.
The Pommeroys were ministers until the middle of the nineteenth century, and the harshness of their thought--man is full of misery, and all earthly beauty is lustful and corrupt--has been preserved in books and sermons.
The entire family seems to have inherited some of this Puritanical temperament, but Tifty has received much more than all the others combined. The others fight against it. One of their weapons is alcohol. There is a lot of drinking done. The mother drinks straight gin and seems to have to stay drunk mainly because of the presence of Tifty, who treats her with scorn. They are struggling throughout the story to have a good time and a joyful family reunion. (Family reunions are always touchy affairs. They bring up resentments from the past. Similar stories could be told about many family reunions.)
There is tension throughout the story, and all of it is caused by the gloomy, negative presence of Lawrence, who arrives on the ferry very early in the story. The tension finally erupts into outright hostility when the narrator and Lawrence are alone together on the desolate beach. The actual violence comes as a big surprise, since it has been so subdued, ignored, avoided, and understated up to that point.
"Come out of your gloominess. Come out of it. It's only a summer day. You're spoiling your own good time, and you're spoiling everyone else's."
(This is the essence of the story.)
Tifty gives the narrator many reasons why he feels gloomy at this supposedly happy family reunion. He criticizes his mother and his siblings and finally says
"You're a fool."
"You're a gloomy son of a bitch," I said. "You're a gloomy son of a bitch."
The narrator hits his brother over the head with a root and is deliberately trying to kill him. He wants to get his brother out of his life and thoughts forever. He wants to say "Goodbye, my brother" for the last time in their lives. But Tifty is only stunned and bloodied by the blow. He and his family quickly depart on the ferry.
The next morning the narrator wakes up. Evidently he does not feel guilty. Rather he feels vastly relieved that he has gotten his brother out of his system with his violence.
...I got up and went to the window, and what a morning that was! Jesus, what a morning!...The air was clear. In the early heat, the roses in the garden smelled like strawberry jam.
The tension, the bad vibes, that have existed throughout the story have all disappeared with the disappearance of Lawrence on the ferry boat. He has told his brother he is selling his equity in this summer house and is never coming back. He will probably never see any member of his family again except at his mother's funeral. He is good about attending funerals.