I'm in the "listen to your mother" camp, only because you simply can't afford a confrontation with her about this kind of issue. IMX (and I am not a parent, although plenty of my friends are), parents have good reasons for restricting their children's conduct. However, if possible, I might try to have a mature discussion about this with your mother about the right age for D&D. Perhaps show her this thread (I imagine many of the people posting here are of her generation or approximate age) and ask her what her concerns are, and if we can respond to them. Is her concern religious (i.e., that D&D encompasses symbology of a potentially religion-related content that may encourage non-Christian behavior)? Is it a concern about the violence inherent in the game? Is it that the game is too mechanical or competitive? Let her explain why she's worried, and then perhaps the two of you can figure out what the right solution might be.
As for me, I started playing when I was 6 [1980], in my friend's older brother's group (older brother in question being 14). No real issues with handling the game, but I was always precocious (we played Village of Hommlet, and then G1-3). A very PG-oriented description of violence (foes were always "defeated" or "knocked down") and no obvious sexual content. I personally don't remember the mechanics being particularly tricky either; I was already playing Chess, Scrabble, and Stratego by that point, and I distinctly remember rolling up my first PC (Arroth Strongblade the paladin, Cha 18 boo-ya!) and walking through Demogorgon's stat block and being awed that only a +2 weapon could even harm him, all this before actually playing. Now, all of this may present a different experience for you and your brothers, but perhaps your mother might like to figure out a way to work with all these folks out here in the online community to establish proper boundaries?