I don't see any tax issue here. You and your parents are just sharing expenses for your second home. There's no income to report either for you or for them. And there's no gift involved because you're just paying bills for a home that you own.
As @Mike9241 stated, if you itemize then you can deduct the mortgage interest and property taxes on your Schedule A, subject to the usual IRS limitations.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
