Robin is fired. When you disobey a direct order that’s what you should expect. Done.
However, was Batman a little hard on her? I know, I know. Batmen said don’t disobey. I got that—but has Tim never disobeyed?  Good grief!, he left—he has a loyalty issue. Dick left too. Did they never have differences? But, no, a girl comes along and he has zero tolerance.  I think he was biased from the beginning. And in someway, it was because DC didn’t want to have a “girl wonder†for very long. I just thought that it was kind of harsh.  I’m a softy.
The bottom line is, if Batman ever offers you a job don’t disobey…he’s not very patient.