The first thing that jumps out at me throughout your post is that so many of your conversations were over the phone. Keep in mind the following: If it's not written down, it didn't happen. Try to avoid having phone conversations. And if you do have a phone conversation, keep good notes, then send a email with those notes to the person you spoke with stating "this is what we discussed in our conversation on such-and such a date." Especially include anything the school district (by way of the person you spoke with) agreed to do or refused to do.
Second, no, your daughter does NOT need to change classes in order to receive an IEP evaluation. That's just plain ridiculous and wrong. If their reasoning behind this is that she has to have an intervention first (as you state above), that is also completely wrong.
My advice going forward:
1. Email (EVERY request should be in writing from this point forward) the director of special education requesting a special education evaluation and explaining the roadblock you encountered at the building (school) level of the need for intervention and changing classes (which you have researched and discovered is incorrect).
2. Include in the above request anything that would support the need for an evaluation (anxiety diagnosis; standardized testing, screenings, assessments showing low academic, reading skills/level; comments/emails from teachers that she is struggling (even going back to grade school); the email from the counselor stating that she may have a specific learning disability; etc.
3. Request an evaluation in the following areas: Intellectual/Cognitive (this may be denied if they already have an IQ test on file, as those results do not change much); Social/Emotional/Behavior (to address the anxiety); Academic Achievement (to address the possibility of a specific learning disability).
4. Request from the principal the following documents: all standardized test and screening results; all progress monitoring results from any interventions (even going back to grade school); all 504 evaluations (even if they were "lost," you need something in writing to that effect); a Prior Written Notice that the special education evaluation is being denied because of no intervention (if they are refusing to do an evaluation because you won't switch classes, you are entitled to a Prior Written Notice stating this).
5. If you ever hit a "wall" with anyone, please remember that everyone you deal with has someone in the district they report to. If you can't get anywhere with the principal, find out who the principal's supervisor is and email him/her. Keep going up the chain of command.