How does it end?

"Goodbye, My Brother" ends with the narrator expressing a vast relief to have finally gotten his pessimistic, misanthropic, negative brother Lawrence out of his life and out of his system. The words "Goodbye, my brother" apply both ways. The narrator says goodbye to his brother, but his brother has already said goodbye to him and to the rest of the family. The narrator wakes up on the morning of Lawrence's abrupt departure with a feeling that a black cloud has blown away and left a perfectly gorgeous day.

Jesus, what a morning! The wind was northerly. The air was clear. In the early heat, the roses in the garden smelled like strawberry jam.

The blustery Atlantic air seems to play an important part in the story. It is as if that cold ocean air has blown away the gloom that Lawrence ("Tifty") brought with him from Albany. The narrator does not even express any guilt or regret over the fact that he had tried to kill his brother on the beach the day before by hitting him over the head with a waterlogged tree-root. Fortunately for both of them, he hadn't succeeded but had only stunned his brother and left him bleeding. Apparently Lawrence did not really resent the blow. He might have been asking for it, even expecting it. Such a blow was what this man expected from life.
Many famous writers have commented on the relief that can come from terminating a destructive relationship. Here are three pertinent quotes:

Do not keep on with the mockery of friendship after the substance is gone--but part, while you can part friends. Bury the carcass of friendship: it is not worth embalming.William Hazlitt
It’s no good trying to keep up old friendships. It’s painful for both sides. The fact is, one grows out of people, and the only thing is to face it.Somerset Maugham
A relationship is like a shark: it has to constantly keep moving forward or it dies. And I’m afraid what we’ve got here is a dead shark.Woody Allen

This was supposed to be a big family reunion. Big family reunions often turn into big family debacles, especially if a lot of drinking is being done. Everybody dreaded the arrival of Lawrence, including his own mother, who had to stay drunk on gin during most of his visit just to be able to tolerate him. Nobody was sorry to see him go. It did not seem likely that they would see him again except for his mother's funeral. He is the kind of man who would be punctilious about attending family funerals and would probably enjoy them.