I have a few opinions on this and I ask that you keep an open mind as you may not fully agree. One of the biggest issues that I see here is that you are very demanding that your doctors conform to what you want, even if it may not be what you need. A lot of the criteria for meeting certain treatments are dependent on what you have already done to work towards resolution/management of your issues. The moment you start demanding is a red flag to most doctors and a lot of times they will do the complete opposite unless what you are demanding is deemed in your best interest by a board licensed psychiatrist/psychologist. It could very well be that your doctor doesn't feel that your particular situation warrants what you are demanding.

I want you to take a few minutes to ask yourself the following in your head.

Have you done everything possible to manage your illnesses?
Has everything you tried failed?
What exactly do you think that a service animal will do for you?

It also could be that the cost of a service animal outweighs the costs of untried therapies. It could also be that they are unsure of your diagnosis and they aren't sure how an animal will help you.

I am in no way saying that you should not have a say in your treatment. You know yourself much better than anyone else. But the one thing that is obvious here is that it seems like you have a trust issue when it comes to doctors and their ability to treat you. While I can appreciate that you are trying to get what you think may help you, your demanding demeanor, especially your demands for meds can come off as "seeking" behavior, which throws up a huge red flag in the faces of any responsible doctor. Try calming down and approaching things with a calmer attitude and work with them rather than against them when they are making decisions in what is their professional opinion of your best interest. Hope this helps and I really hope that you get the most out of your treatments.