ok...if you are making 20K as a 15 y.o why are you posting complaints about your mom when, obviously, you have no problem buying the thing in the first place and you seem to have control over your finances? were you looking for some sort of affirmation from faceless strangers? it seems that your concerns don't seem to have a valid obstacle between what you say you want and having the resources to buy what you want/need so i find no reason why you are raising an attitude when you could have bought the thing in the first place.
interesting that you say you earn 20K at 15 considering the legal working age in the US is 16. even if you teach piano, IRS tax filing status still requires you to be of age to work given that you are earning a substantial amount of income. i teach guitar and drums and have done so for 12 years so I know the books on this one. a quick search of older threads you've took part in suggests that you are in the US and thus subject to standard US labor laws and tax filing requirements. besides, i never suggested that you give up however you earn your money because i neither care nor inquired about it.
whatever the case, get your money, buy your laptop - however much it'll cost you - and enjoy. parents will say weird things from time to time, this is natural, give your mom a break...a lot has changed since computers became mainstream items and it was virtually unheard of to have a home computer in the 60s and 70s so teach her to be up with the times and lay off the hate-o-reade. your mom carried your @ss for 9 mos, the least you could do in return is teach her about a mac for chrissakes.