It's a lot of information and emotions to process and absorb. And it takes a while. You've played the scenario out over and over. For your Mother, this is all new. Her reaction perhaps hadn't been as well thought out. Knee-jerk if you will. Time is always on your side. As stressful as it may have been, coming out as you have done is one of the most liberating and empowering things one ever experiences, a burden that you had been carrying for a while. Kudos to you for this huge step!
On the religious aspect of things: Your Mother is absolutely dead on, God does not make mistakes. Not one. Never. It clearly states this in Genesis 18:1-33. When he made you, he did not error either. He knew exactly what he had done, what he was putting you thru and His plan for you. You now are simply re-affirming that plan. (my son, one of four, my lone supporter...very much a Christian...have had many talks about this...and it was he who clearly explained this point to me) Another point to ponder here is this, and this is my own view, perhaps not shared by many: Our world is shared by over 7 billion people. Nearly all of them believe in God. Thru the ages, all cultures, no matter how primitive, have worshiped a God. God has been an integral part of who we are. But, there can only be one God, shared by all of us. And as much as we may like to feel that our God is the only one, the other guys God is the same one too. Always has been. Another little tidbit here: Some people's God have no problem with transgendered. As a matter of fact, they are celebrated. Number-wise, we're looking at 1.4billion people, or five times the population of the United States.
So, be happy with who you are. Stress your happiness to your Mother. And surround yourself with as many happy and positive people as you can.