I don't think the giant Joker playing card has an origin...it just is
Batman probably just got it as a constant reminder of how much he hates the Joker. Gotta fuel the brooding.
Edit: First post of the page, so I'm gonna repost this, because nobody seemed to notice it before and I feel like it's fairly big news...
Jason Aaron and Ron Garney doing a book about a hitman: "Men of Wrath."
Let's move to the protagonist of "Men of Wrath," the hitman, Ira Rath. What can you tell us about Ira? What are his goals when we first meet him?
Aaron: He's a bad guy. He's an older guy who's reaching the end of his life, which consists pretty much of killing people for money and living alone in an empty house which doesn't have much furniture. For him it's clearly not about the money. There's something else going on.
"Men of Wrath" is about a family history. So each issue opens with flashbacks to different generations of the Rath family. We kind of start to see how the cycle of violence begins and gets perpetuated and passed down from generation to generation of this family and kind of culminates in Ira as the worst of the bunch.