The difference is that Remy is a legally appointed law enforcement officer, and Batman is a dangerous law breaker.
If you have ever been pulled over? The cops ask you to keep your hands where they can see them for a reason. A car has plenty of places to conseal a weapon and Batman probably even has more inside his belt!
So yeah, justified shoot. He's a known law breaker/fugitive, he is defying a direct police order and assaulting Penguin. Even if Penguin was a convicted criminal, Batman has no right whatsoever to lay a finger on him when Penguin's not hurting anyone.
Batman's a vigilante, he should accept by now that he doesn't have the same rights as everyone else. But instead, he's just rubbing their nose in his superiority. That's pure bullshit.