If you are there to secure a letter, you are not there for therapy, you are there for a letter. How honest have you been with her about your goal?

Her responses around childhood sexual abuse sound cruddy and I would not continue working with her for that reason alone. You certainly should not be feeling like you are the problem.

Perhaps as importantly, have you been able to effectively explore the issues around your gender identity with her? It doesn't sound like you would feel safe enough with her to dig into the difficult questions of perceived gender versus biological sex.