Update - Feeling better about the VA's gender therapist

OK, I just got back from talking with Dr. Israel for the second time, and today things went better. She still has not gotten in touch with my other therapist, but says she will do so before our next appointment in two weeks.
 
She now understands why I refuse to do online therapy sessions, and is ok with that.
 
We had a good long discussion, more a "getting to know" each other, during which she said things that told me she really DOES have enough of a clue about gender issues to help. I'm thinking that last time, she and I were both reacting to being thrown together by the system, she trying too hard to win me over, and me still feeling betrayed by being forced to start all over again with a unknown therapist.
 
Some things she said put me at ease on subjects I have previously kept to myself; so maybe this will work out after all.
 
Transitioning is a complex and difficult process, made more so by all the mental and emotional baggage from my former life. There are still issues I need to deal with, and things I need to address - some things I just need to purge so I can get on with being myself at last.
 
All in all, I feel better about continuing to see her now. We laid out a rough outline of how our sessions will go, and plotted out what the main topic of the next session will be.
 
She also explained why she had asked certain questions last time, telling me what my answers translated to in telling her who I really am inside.
 
I'll take it a day at a time, for now. But it is looking a bit better.