Lol, its not hard, all you do is open the case and blow!
Tell her that. Infact, tell her that you will walk her though it while you do it. Or even better, tell her exactly what you are going to do, and ask if she approves, and if she does your in the clear, and if not just wait. Because I guarnetee you that she wont open up the case, and check to see if you did it or not. So really you can do it either way.
Dont worry, when I was 14 my mom didnt trust me to make my own computer, so we wasted needless money on the Dell. Just give it time, your mom will learn to trust you as you get older.