I have a couple of contributions to make to this thread.
First of all, Hal is alienated by his father, who he never had a relationship with, except for when he said he was reading the paper, drinking coffee, and talking to Hal all at the same time. The rest of his family still treats Hal ok, but have always disagreed with his choice of wife, so they almost never see each other due to the tension caused by the family's hatred for Lois.
Hal and Francis are A LOT closer than Hal and his father. One of the brilliant strengths of the series is how the parent's--especially Hal's--love for their kids is conveyed. One particular scene in Hal's Birthday puts me in tears everytime:
Francis: "It was just so quick, you know? If you know you're with the right person, why not go for it? Why not get married?"
Hal: "I would have come, Francis?"
Francis: "What?"
Hal: "I would have come to your wedding. If I was invited, I would have come."
Francis: "I'm sorry."
And complete silence.