Congratulations on the coming out. I'm in a similar situation with my mother. When I told her she said almost exactly the same things as your mother.
Due to number of reasons I couldn't really start transitioning right away after my coming out, just made small steps. And now I know what a mistake that was.
I should have pushed it with full force. Because I don't talk often with my mother and because I don't mention transition in every other sentence, she thinks I may not be serious about it.
So now my mother is just sinking into denial about it, she saw my clothes, she saw how feminine I look, she is even willing to wash my women's clothing and she still calls me her son after almost a year. She can't see the girl in me yet, but who know me as a girl, can't see the man in me.. Strange situation.
I need to step up my efforts, and you shouldn't wait either, because most probably she will think it was just a phase, she can even dismiss official diagnosis saying that the doctors are incompetent.
You need to provide your parents with all the information about transsexualism you can. They need to understand it is not just a phase, it is not easy for you, it is not their fault, and it is absolutely vital to your well-being to move forward with your transition.