Time, patience, reflection, and realization will become very imporant things inside your relationship. Patience with her, and patience with yourself.
I think it is important to remember Emma when you have these thought. How would Emma feel if she knew how I felt? We look upon our SO for comfort, reassurance, safety. For many folks who are transgender, their SOs offer that comfort that feeling of its ok to be "me". For Emma, I assume that is what she is hoping for.
Everytime you catch yourself criticizing her, or questioning her identity, stop and reflect. Why am I thinking like this? What is going in at this moment or at another time that made me think like this? She is a woman, and I am pretty sure Emma would be very heartbroken if she heard you talk like this. And i know you don't mean to hurt her. This is going to take action from your part. Self reflection is important, be patient with yourself and Emma. Forgiving myself also became something I did a lot, for hurting Sarah, for not being the person I knew I could be. But in the end, I knew I had to work on being a better SO.
The first year for Sarah and me was a bit of a challenge, and that was even after a year of learning about trans* issues and information. I had to actively break a lot of stereotypes I still had, and analyze my belief systems.
My beliefs aren't perfect and I still work on being a better. Heck, I'd like to read what other people comment because it gives me a fresh perspective and a way to be a more supportive SO.