Of all my family and friends, my Mom has been the most difficult. Even now, after living full time for almost 2 years, we're STILL at odds over my decision to make such a drastic change in my life.
It's important to realize that most of your family will probably view your transition as a horrible tragedy. In their minds, it's like throwing away a perfectly good pair of shoes just because a new pair might appear more attractive. They also see it as really that simple... that you can simply "fight" your "urges" to live as a woman. They'll link what you're doing to your sexuality and suggest that you just need to "man up" and try being more masculine to cure yourself. I'm sorry to say it but you lose all credibility with family when you come out as Trans... According to them, you've lost your common sense and anything you say is suspect.
I think that my most valuable defense was information that came from outside the situation. I bought my Mom a book that helped lots... "True Selves: Understanding Transsexualism: For Families, Friends, Coworkers, and Helping Professionals" by Mildred Brown became a useful tool. You can get it for under $10 at Amazon. The notion if transsexuality is frightening to many people... Try to stick to the facts when talking to her about it and avoid reacting to her negativity. She's reacting the way she is because she loves you and doesn't want bad things to happen to you.. that's just what a Mom does. After things calm down, consider inviting your Mom to see your therapist with you. Sometimes it takes a person sitting behind a desk with certificates on the wall to "prove" that what you're experiencing is real.
Good luck.... Try to be patient and give it time... LOL.. My Mom knocked on my door just now and asked what I was up to.... I told her that I was trying to offer advice to another woman having issues with her mom.... She just shook her head and went back downstairs

I love her dearly but I know that she'll never really get it... but I know that she loves me.