Hello JustinH2
Thank you for your question.
As a US Citizen / Resident, no matter where you have rental earnings, these will need to be reported on your taxes. It does matter whether the money comes to USA or goes towards paying a mortgage in Denmark.
Please refer to Rental Real Estate and Taxes article to learn more about this subject.
When renting to family you need to make sure that you are renting it at fair rental value. If you not renting at fair rental value or renting 'below market rent' this is considered personal use and you can deduct your rental expenses only up to the amount of your rental income.
If you have any further / specific question, please do let us know.
Thank You
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