Yes, your therapist sounds like a bit of a wet rag if she doesn't even have the common sense to figure out how to write the letter. She's happy to take your money though...a shame you can't move on to another one really, but we have to work with what we have at our disposal.
So as Dee pointed out, you're going to have to do the leg work for her. Find some sample referral letters, print them out, etc. And if she still can't handle it, go straight to your primary care physician and talk to him/her instead.
I'm not a huge fan of "teaching" the therapist. While a good therapist should be able to apply their training and experience to many situations, I think that gender identity disorder is an unusual area because the therapy is often diagnostic rather than curative, and you're not going to therapy to make the dysphoria go away; you're going there to have the therapist confirm that it exists and pass you on to the medics who can give you what you need.
(That said, therapy in my case has been wonderful in getting me to come to terms with my own gender identity disorder, and I would not have skipped therapy for anything. It's good to talk to someone who truly understands what we're going through, because without that mental support, things get hopelessly crazy sometimes. You don't have to think of therapy as merely a hoop to jump through on your way to HRT, because done well, the therapy process is life-alteringly amazing.)