Raizen is not literally Yusuke's father, but his ancestor through Yusuke's mostly-human father, who from all indication, did not realize he had demon blood. Yusuke's mother and father had a bad relationship and split up, leaving Yusuke with his mother.
In the manga, there were a few chapters after the Demon World Tournament that weren't adapted into the anime (rightly so, because they weren't good), but they had a few nice moments. One being Kuwabara actually taking part in a mission with the team and being useful (the mission was lame and rushed, but still), and another being a short appearance by Yusuke's father. We don't learn much about him, but we get a better view of his relationship with Yusuke and his mother. He and Yusuke's mother see Yusuke from a distance. Yusuke's mother tells him not to talk to him, otherwise Yusuke would get angry and try to punch him. Yusuke's father makes a reference to hitting him as a child, and I'm not sure if that was meant to show abuse or it's a cultural thing. Yusuke's mother says they should go out before she remembers why they split up in a few hours, like usual, and they walk together with her smiling.