YES! set up a partnership, or you might find yourself in a "defacto" partnership under the generic rules, and liable for business debts that you never intended. Losses in a partnership can also be claimed against other income, so if it loses money (today), then pays off in capital gains later, that is to your benefit too. (shifting taxes to the future)
Also -- as she is living and managing it on site, her unit could be considered a cost of the business, even partially. Also good for tax deductions on the business income.
Generally, you can't structure your partnership unconventionally, to deliberately minimize taxes that are paid.
You are allowed to reduce your taxes to the full legal extent, but not to structure a deliberate tax evasion.
You could set it up so that you each have 1/3 value, or a pro ratio value of the capital and the income, according to each person's original contributions, then that is fine. Can't change this partnership structure without a real reason (other than tax avoidance), and should file papers stating the partnership structure (along with how to dissolve the partnership! don't forget that important part).
e.g.,
If you wanted to, you could do a break out like this. Talk to an accountant, too, to determine if net profits are before or after your sister's share of rent is paid... typically I would value ( a modest amount) into the equation and subtract it from her portion before distribution.
Mom -- has a 50% share of capital gains and a 10% share of net profits, as she is contributing 50% of the downpayment, and co signing the lease.
Sis -- has 10% share of capital gains and 70% share of net annual profits, as she is contributing time, no capital upfront, but co signing lease.
Me - has 40% share of capital gains and 20% of net profits (the remainder), and is not co signing the lease, but contributing management support on occasion, and 50% of the down payment.