Why does Christine call her father Charlie?

She calls him "Pop," most of the time, but refers to him as Charlie, although she does occasionally call him Charlie. I think it has to do with the fact that as adults, they travel in the same social circles. Most people, when they say "My father," are referring to someone the other person doesn't know well, or at all, but because they both socialize in cop circles, everyone knows Charlie Cagney, she's used to hearing other people call him Charlie, and when she refers to him as Charlie, she is sometimes talking to people who have known him longer than they have known her.

I usually refer to my mother as "My mother," but when I am talking to my husband and step-father, sometimes I refer to her by her first name, because they are. When I am with her colleagues, I refer to her as "Dr. Goldhammer," because they do.

It's all about context.

Plus, as adults, the Cagneys are friends, buddies, and I think the "Charlie" communicates this. The fact that Brian doesn't do this shows us that his relationship with his father has not grown since he left the house.