A family connection isn't necessarily deep.
This guy's pretty much got it down:
The main thing to understand is that the real protagonist of the story is the Yakuza with the sunglasses. The film starts with him (I'll call him Yakuza) and Atsu waiting in the car. When they see Myon run by, Atsu gets out and chases her. She jumps into the train, and Atsu manages to get onto the same train so that he can follow her. This ends the first sequence.
Next, the montage of past events begins. This is a chronological run through of all of the events that lead up to the scene in the car that we just witnessed. I'm going to go by the reprise of the montage that comes at the end of the film, because it is more complete.
The first shot is of a bridge. This is the first memory of the baby in the 2nd shot, who will grow up to become the old man from the whale. We see him reach adulthood, where he chooses to lead a life of crime. (Metaphor can be seen in the church shot) We see him have a child (who grows up to become the Yakuza) and we see that he smuggles drugs in children's toys. He is then swallowed by the whale after a drug bust. His wife subsequently dies during the childbirth of Atsu.
We now see his first child, the yakuza, who has grown up. He meets a woman and they fall in love. This woman will become the mother of Myon and Yan. One night at the club, she sees Myon and Yan's father and chooses to go with him, essentially dumping the yakuza. This is what propels him towards becoming a yakuza. (it's unclear what his profession was prior to this) The yakuza spirals into a life of crime, and the woman gives birth to Yan and Myon. However, the father continues his womanizing ways, and pays little attention to his family. Nishi is also born.