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Although you could make such an arrangement as you describe, it will not result in you being able to deduct expenses for the rental in excess of the amount of rent that her friend is paying.
First, use of a rental by a family member that is paying less than fair rental value is considered personal use. For more details see Tax Topics - Topic 415 Renting Residential and Vacation Property (formerly Renting Vacation and Renting to Relatives)
A day of personal use of a dwelling unit is any day that it is used by:
If you use the dwelling unit for both rental and personal purposes, you generally must divide your total expenses between the rental use and the personal use based on the number of days used for each purpose. However, you will not be able to deduct your rental expense in excess of your gross rental income."
Second, the scenario that you describe would seem to be a rental not for profit. Having a family member live rent free in order to rent one half of the house would seem to preclude that the activity was engaged in for profit.
See Personal Use of Business Property (Condo, Timeshare, etc.) for details:
"If you do not rent your property to make a profit, you can deduct your rental expenses only up to the amount of your rental income.
Any rental expenses in excess of rental income cannot be carried forward to the next year."
So, even without getting to the issue of whether or not it would be a valid
deductible business expense to allow your daughter to live rent free in exchange for management services, there are specific provisions in the tax code that will not allow you to deduct expenses that are more than the rent that is actually paid.
You can set it up as you described; but there is no tax benefit to such arrangement.
Compliments to you, though, on trying to pay the least possible legal amount of tax.