I do understand that you are living under her roof, so you have to respect her rules. However, having your phone and computer taken away, which has nothing to do with your relapse, is counterproductive towards your recovery. While she believes that she is being a good mom by punishing you for your relapse, she doesn't see that she may have just hopped on your resentment list.
If my mom took something away from me every time I relapsed, I would have nothing by now. I am ten years older than you, and I really wished I started recovery at your age. Do you have a sponsor? If so, have you bounced some ideas off of him/her? The only thing I can think of at the moment is to have a mature one on one talk with her about how crucial it is to your job. Perhaps you can write some thoughts and ideas down on paper before talking to her? Good Luck.