Fugetaboutit. You don't have a rental, you have family sharing expenses.
If this is merely a cost
sharing arrangement where the amount paid is below fair market rental, there
would be no reportable income to you. If the “rent” amount is fair market
value, or more, there is still some question as to whether you even have to report it, as
it almost always comes out zero. Most people take the attitude that it is not
income; it's just room mates sharing expenses and ignore it. Family, as opposed to unrelated roommates, makes that
position stronger.
What you are NOT allowed to do, because it is your own home (you have
"personal use") is claim a loss from this activity, to offset other
income. Because of the "personal use rule", your deductions are
limited to your income. Net effect ZERO.