You will file an Alabama nonresident return. Exactly what income flows there depends on whether you are renting "for profit" or you are giving your daughter a less than fair-market rental (discounted rent) that would indicate that you are not renting for profit. That is determined on the Federal return, and the net income that generates from that amount is taxable in Alabama as a nonresident. Prepare the Alabama nonresident return first claiming this income. (Note: if you rented for less than fair-market, you have a not-for-profit rental. This is considered a non-business activity, or a hobby. You report the income and it is taxable, but you may not claim expenses against the income.)
On the Alabama return you must allocate, or designate, or assign, that portion of the income to Alabama. Illinois also taxes the income, but will provide you with a credit for the taxes you pay to Alabama on this income. You prepare the Alabama return first, so that the Alabama tax credit can be transferred over to your Illinois return.
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