Both my wife and I file Married/separate. Our current home is in my name and I claim the property interest on my tax. Can my wife claim Prop tax on the rental?

May I ask why you are filing separate returns?  Sometimes people don't realize the differences between filing  Joint and MFS.

 Here's some things to consider about filing separately……

In the first place you each have to file a separate return, so that's two returns.  And if you are using the Online version that means using 2 accounts and paying the fees twice.  

Many people think they come out better when filing Married Filing Separate but they are probably doing it wrong.  If one person itemizes deductions on Schedule A then the other one must itemize too, even if it's less than the standard deduction, even if it is ZERO!  (Business expenses are not itemized deductions.  Business goes on Schedule C not A.)

And there are several credits you can't take when filing separately, like the

EITC Earned Income Tax Credit

Child Care Credit

Educational Deductions and Credits

And contributions to IRA and ROTH IRA are limited when you file MFS.

Also if you file Married Filing Separately up to 85`% of your Social Security becomes taxable right away even with zero other income.

See …….

https://ttlc.intuit.com/community/married/help/is-it-better-for-a-married-couple-to-file-jointly-or-separately/00/25590

Who is claiming the rental income and expenses?  Who owns the Rental?  If you both own it you should probably split the rental 50/50.  Why couldn't she take the interest on both?  Rental interest and property tax go on Schedule E not as itemized deductions on Schedule A.  

The tax payer who claims the rental income, is the one who claims the expenses, to include the property taxes.

Typically, for a married couple to file separate returns means that they pay more in taxes overall. But that's the taxpayer's call.

If both of you own the rental, you can each claim 50% ownership and split all income/expenses right down the middle on your separate returns.

When a married couple files separate, they both automatically disqualify for deductions they would otherwise qualify for if they filed joint. One thing affected (of many) is the EITC, as well as education credits. Also, when filing separate if one of you itemizes deductions, then the other is required to also itemize deductions, even if the itemized deductions of one of you are zero. Likewise, if one takes the standard deduction, then both must take the standard deduction even if the itemized deductions of one of you would be higher.