I'm not one for "Conning" parents. Well,,,,,, maybe I am. Anyway; if she's such an extremist to have locked you and your father out of the house, then reasoning with her about it being "your" decision probably isn't going to help. But what you might try is coming at it from a different position.
1. Make sure that she knows that you are also actively applying to other traditional colleges. (You are, Right?) The academy isn't a guarantee, and I emphasize that every person applying to the academy should also be applying to some big name schools. Not just state U. Nothing against state; but if you think; and are; qualified to be attending the air force academy; then you're qualified to be at Yale, Harvard, Stanford, Brown, etc... Anyway; let her realize that you are taking your education seriously.
2. Mention often how only approximately 14% of those applying to the air force academy will get in. Let her know that these are the same stats as many of the Ivy League schools. And that you understand that your chances of getting in are slim. It will at least realize that you are quite aware of process, odds, and commitment of attending the air force academy.
3. MOST IMPORTANTLY: Emphasize the FACT that you realize that you are still a young man, and that what you "Think" you might like or want today, could possibly change in the future. And emphasize the FACT that the academy realizes this also; and allows any cadet up to 2 FULL YEARS to realize that this might not be for you. You are free to leave at any time up to 2 years. And that you haven't wasted anything, because your credits can transfer to another school if the academy doesn't work out.
What is so important, is that you show your mom through words and actions that you are reviewing your educational options maturely and not only out of emotions. If you show her and ask her assistance with some of the other college applications; she will realize that she can't really complain about your thought process.
Don't try and argue with her about this being YOUR LIFE. Trust me; that means very little coming out of a teenager's mouth when as parents, we have seen ALL OF YOU change your mind about things at least 10 times a day. (And don't take offense; we parents did the exact same thing when we were your age). Instead, you need to SHOW her that you understand your educational and career opportunities and options. Leave a lot of civilian universities AND Air Force Academy literature around. Let her see all of it. Let her see scratch paper work sheets where you are figuring out the COST of the civilian schools; VS the 9 year commitment of the academy. Let he SEE that you aren't taking any of this lightly. Don't TELL her this; it doesn't count. You have to show her, WITHOUT ACTUALLY SHOWING HER. And again, DON'T FORGET TO ASK HER ASSISTANCE with the college applications, essays, recommendations, filling out financials, etc... Best of luck... Mike.....