If there was no trust:
You are describing an arrangement where you are acting as an agent for the owner. As an agent, you can't claim depreciation as an expense, only the owner can do that. You can claim expenses you pay for, but not expenses the owner pays for. (Who pays the utilities? Who pays the property insurance? Who pays the property taxes?) A more typical arrangement would be something like, you handle the arrangements and keep 50%, and the owner gets the other 50%. You would file a tax return as a rental agent, and the owner would file as a landlord. You can adjust the percentages so that you keep most of the money, but the owner needs something against which to deduct depreciation and anything else they pay. I would recommend tax advice even in this simple arrangement, at least to get it set up properly, and you would want to put the arrangement in writing in some form for mutual protection.
Because of the trust, you really need a professional. And because the trust involves family, you really really need a professional. Messing it up might cause emotional injuries that would be hard to heal. The grandmother might not be allowed to rent, or the trustees might be entitled to split the income. Or the trust might only be to protect the home while she lives there, and moving out might trigger a requirement to sell or some other provision.
