Why do you and your mom want to treat this as a business relationship at all? As a practical matter, kids fixing stuff around their parents' house and parents giving kids money is just something families do for each other, and I would not bother to report it at all.
The other issue is whether this is an "ongoing trade or business" that you operate in a businesslike manner with a clear profit motive. Do you do contractor/handyman work for other people, or only your mother? If only your mother, and you insist on reporting the income, it would be other or hobby income and not self-employment. You would not owe self-employment tax, but you can't deduct expenses like tools and so on. (If you are reporting this as a business, so you can deduct tools as a business expense that are really for personal use, since you don't do handyman work for anyone else, the IRS may view that as improper if you are unlucky enough to be audited.)
