Get a practice pad. Work on that, it will help you build up some skills and it's tiny and quiet.
Learn to read the music. If you still like it then join the school band. Talk to your band teacher and see if they will let you mess around with their kit after school.
Make friends with a drummer and have them let you use their set.
You should be able to fit a set in your room, you can save a few bucks and buy one on your own. Play when mom isn't around. Also, if you get a set, you can buy pads for your cymbals and drums and that will greatly help in reducing the noise and let you get a feel for playing a full set. A drawback to that is that hitting the pads doesn't feel the same as hitting the drum heads.
Maybe if you demonstrate a real commitment to it your mom will be more receptive and help you buy one and tolerate your playing. Stick with it if you like it. Parents can surprise you, I didn't think my parents would be keen on me wanting drums but my grandparents bought me a set and my parents tollerated it and even paid for lessons.
I've seen a lot of suggestions to get electric drums. Electric drums are fun but I wouldn't recomend buying a set. First of all they're too expensive. Second, it's just not the same as playing real drums. I've played drums for years and I'm only a mediocre drummer, though on an electric set I'm able to make sounds that I could never do on a regular set. It's just not right. Also, electric drums are pretty cheesey. I don't think I've ever been to a concert where someone was playing electric drums, they're a fun toy but overall they're kinda lame.
Good luck!