Hmm! Right now your mother is probably thinking Bl**dy kids!

She is probably concerned that you might possibly need to use your money for 'other' things and that feels putting so much of your money into this venture isn't a good idea.
You will just have to prove to her that you CAN be an adult that can be trusted and try not to behave in a sulky manner whilst showing her that you CAN manage your money.I reckon that with your father on your side that eventually you will get Sky without having to dip into your own pocket.Eventually you may actually gain financially.Frankly the time WILL fly (July is only 5 and half months away).
However a word of advice, don't nag.Us mothers just dig our heels in if our teenage sons nag and we get very stubborn.
Incog.