First thought, Maggie didn't like either JC or the police and wanted to encourage a conflict between them, in keeping with her Modus Operandi.
JC shoots the police, she can now get someone in their to destroy evidence or something other scheme.
Police shoot JC they've solved a problem. JC comes out a wanted man, makes his job harder.
JC decides not to break in to the vault maybe he believes her and becomes part of the conflict between the triads.
The fight in Versalife is a bit mad. I can assume she's never lost a fight to the death before and that gave her confidence.