My mom won't let me dye my hair?

I'm 13 years old and I want to dye my hair a dark-ish brown. Right now I have hair that's sort of in-between light and medium brown hair with natural blonde highlights. I want to dye my hair darker bcause I think it will look really nice with my skin and eye color, and also I just got braces and I think it'll work a lot better with them than my current color. However, one of my friends is always dying her hair really badly and it looks terrible on her because she dyes it unnatural colors like orange and black (which doesn't look natural because she's pale with green-blue eyes) and then doesn't take care of it so you can see her roots. My mom says that she, and i quote, "looks like a cheap hooker". I have no clue how my mom drew that conclusion but anyways, because of her I'm not allowed to dye my hair. I can get a streak in it, like a blue or purple streak, but most of my hair has to remain this color. I think that is 100% unfair and unreasonable. The reason I want to dye it is because she forced me to get braces, which I absolutely did not want (my teeth aren't even crooked). Besides, tons of kids at my school dye their hair and look great with it. It's just that the only kid she's seen with dyed hair does it terribly and doesn't take care of it. How can I convince her to let me dye my hair????? I'm half considering riding my bike to the store and just getting a box of dye, just because she is ALWAYS doing stuff like this. Like, last year she took me to the store to buy summer clothes, and picked out most of what I bought. Now this year, after barely growing at all, she complains that everything I wear is innapropriate even though everything I'm wearing is what she picked out for me. Mostly it doesn't really matter to me, I don't care about wearing longer shorts and stuff, but I really want to dye my hair.