I really wish I'd had advice like this when I was Roc_Kor's age.
Roc, I hate to say it but everyone here has the right of it. Moms have a terrible thing about the spirit of her law being even more important than the letter of it - and handing your pal an AK in the garage is going so hard against the spirit of it that the letter won't matter an iota.
Look at it this way - as a 15-year-old ambassador for responsible gun owners of all ages, you've got a prime chance to show her how responsible, mature and intelligent you are.
Also, as much as it may stink (sure did when I was 15, I'm not so far o'er the hill that I can't remember it), her house - her kid - her rules. Believe me I know - it's a major pain.
I say leave it alone. The more you push things, with a certain type of person (and she sure sounds like the type), the more the inputs to their brain squeeze shut, until finally all she has to do is hear the sound of your voice to have a "no!" forming on her lips.
Heck, try paintballing. It's good exercise, good fun, great for the hand-eye co-ordination and situational awareness. The ammo's cheap, the markers tend to be cheaper than firearms and, as stated, having more than one hobby's good for you.
Hope it all works out, chap.