You say they are the owners, but then say that the house and loan are in your name.
It sounds like this would not qualify as your second home.
It also sounds like it is a rental.
If the relatives are reimbursing you, and you claim the interest, they, in turn, are paying you interest. And you in turn would need to claim that interest as income.
The same would hold true for the property tax.
If this is your second home, and you do not rent it out, enter the interest and tax under
Deductions & Credits
Your Home
If this is a rental, enter it on Schedule E
If it is neither, don't report the interest paid.
According to the IRS, in order to claim the Home Mortgage Interest paid as an Itemized Deduction:
"For you to take a home mortgage interest deduction, your debt must be secured by a qualified home. This means your main home or your second home. …
Main home.
You can have only one main home at any one time. This is the home where you ordinarily live most of the time.
Second home.
A second home is a home that you choose to treat as your second home.
Second home not rented out.
If you have a second home that you don’t hold out for rent or resale to others at any time during the year, you can treat it as a qualified home. You don't have to use the home during the year.
Second home rented out.
If you have a second home and rent it out part of the year, you must also use it as a home during the year for it to be a qualified home."
The loan must also be secured by the property.
"In other words, your mortgage is a secured debt if you put your home up as collateral to protect the interests of the lender. If you can't pay the debt, your home can then serve as payment to the lender to satisfy (pay) the debt. In this publication, mortgage will refer to secured debt."
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