If you were Batman, Would you break your one rule for the Joker?

I watched Batman under the Red hood for like the 52nd time and I understand the batman has one rule that make him different for the criminals of Gotham. What makes a great Villian is someone make you feel hate. A Villian isn't someone you're supposed to like. Only two comicbook Villians Gotten me to that point of hatred, Lex Luthor and the other the Joker. To be into comics you have to have huge imagination. Some people think Lex Luthor is a cool Villian but imagine if that person was real. Imagine someone who was so greedy for Power and Respect that they would put millions of lives in jeopardy for it. Imagine someone who always want more and it doesn't matter who he has to kill or steal from or align himself with to get. That's not cool. That guy needs to be stopped.The world will always need superman as long as Lex Luthor is still alive. Superman knows that but he has a rule too But there comes a time where rules need to be broken and Superman may have to make an exception.

Now Batman on the other hand, this guy has no tolerance for crime, but killing should be the ultimate No, No, Considering how much Death surrounds him most of which The Joker is Responsible for. I watched Tim burtons Batman where The Joker was responsible for the death of his Parents. I watched The WB T.V Show Birds of Prey where the Joker was responsible for Barbara Gordon being paralyzed from the waste down. not to mentioned he murdered Commisioner Gordons Wife and kid and made Him watch while he did it. Now watching the Dark knight Where he murdered Bruce's childhood best friend Rachel Dawes and disfigured Harvey Dents face. He blew up a hospital and threaten to blow up a Boat load of people if they didn't blow up themselves. Why did Joker do it? I don't know. Why don't I know? Because he doesn't even know. He's like a dog chasing a car he wouldn't know what to do he caught it....He just do!Now after watching The Red hood,where He murdered Batmans Sidekick Robin (Jason Todd). That's where he should have drew the line. Not only was he Batman's sidekick but he was a sixteen year old kid and he showed no remorse. Jason wasn't asking to kill Two-face or Penquin or the riddler he was just talking about making an exception on the person who caused not only gotham but batman personal misery. Jason was right you can't stop crime you can only control it. In my eyes batman isn't willing to do what he has to do to protect Gotham but Jason was, and that's where they bump heads. Batman has to know that as long as joker is alive more lives will be takened and that's more blood that will be on Bruces hands. If you're going to be gothams protector, You have to do whatever it takes to protect the innocent people of that corrupt city. Being sentenced in Arkum Aksylum isn't enough for some criminals,The joker in particular. So,I'm asking you, If you were Batman, Will you be willing to break that one rule for the Joker?