I think the first thing is to make sure the student will cooperate with an IEP if he is given one. If he "doesn't want any help at school," does this mean he doesn't want to be pulled from the general education setting and go to special education? If he can't be talked into this, I'm not sure it's worth the fight to get an evaluation.
When you say "the support" is not helpful, do you mean specialized instruction that students receive via an IEP for dyslexia or accommodations via a 504 Plan? Could the parent consider private tutoring? A student is usually given a brief evaluation before the tutoring begins with no obligation to sign up for tutoring.
As far as the timeline for requesting another evaluation if denied, she should request an IEE, file a state complaint, and/or file for due process based on the fact that the school was presented with a diagnosis of dyslexia (and other data showing struggles) and refused to evaluate.