Wow, our mothers would get along. I came out to my mom when I was 17 and she said the exact same things to me. It's going to be a slow process and you just have to give her time because she'll eventually come around.
This is how it went with my mom.
-Stage One: she pulls every possible excuse out of her ass (the whole "Oh you're just an insecure teenager. All teen girls are uncomfortable with their bodies! You don't know what you want, you're too young"). This stage lasts quite sometime.
-Stage Two: It starts to hit her a bit so she bring up all these examples about how you aren't actually trans because it's a phase. "Oh remember that one doll you played with for 5 minutes 10 years ago? Or that pink shirt you wore a couple of times when you were 3?!"
-Stage Three: She gets pissed off and yells at you about it. Threatens stupid crap that you know wouldn't happen. My mom's threats: burning my mens clothing, selling my car, kicking me out of the house, changing schools, not helping out with college.
-Stage Four: Hits her with a ton of bricks. She's finally realizing that it's true and kind of gives up because there's nothing she can do to change your mind. (Gave me approval for starting T just before my 19th birthday)
-Stage Five: Finally realizes that your happier by going though this. (Just as I'm turning 20)
Like I said, this is what happened with my mom, so your experience could be totally different. It's a grieving process and you must keep that in mind, giving her time and space to process. Eventually she'll realize she doesn't know everything.
Maybe try getting her this:
http://www.amazon.com/Transgender-Child-Handbook-Families-Professionals/dp/1573443182It's basically transkids for dummies. I read the night before I gave it to my mom and it explains everything really well. From early childhood signs, to how it feels to be a trans kid, school issues, and finally hormones/surgery.
If you need to talk/vent or anything, feel free to message me. I'm here to help