Are you sure she doesn't qualify for Head of Household?

IRS has information about this that is so important  they shout it. 

 https://www.irs.gov/newsroom/international-taxpayers-filing-status-if-married-to-a-nonresident-alien... 

IF YOU DO NOT TREAT YOUR NONRESIDENT ALIEN SPOUSE AS A TAX RESIDENT, YOU CANNOT USE THE MARRIED FILING JOINTLY STATUS.

HOWEVER, YOU MAY QUALIFY FOR ANOTHER FILING STATUS.

OPTION NUMBER TWO IS TO FILE AS HEAD OF HOUSEHOLD.

IN ORDER TO QUALIFY FOR THIS STATUS, YOU MUST HAVE PAID MORE THAN HALF THE COST OF KEEPING UP YOUR HOME FOR THE YEAR.

IN ADDITION, A QUALIFYING PERSON MUST HAVE LIVED WITH YOU IN YOUR HOME FOR MORE THAN HALF OF THE YEAR.

TO FIND OUT IF YOU QUALIFY, USE WORKSHEET 1, “COST OF KEEPING UP A HOME,” IN PUBLICATION 501 TO DETERMINE WHETHER YOU PAID MORE THAN HALF OF THE COST OF KEEPING UP YOUR HOME.

YOU CAN USE TABLE FOUR IN PUBLICATION 501 TO SEE IF YOU ARE A QUALIFYING PERSON.

ANY PERSON NOT DESCRIBED IN TABLE FOUR IS NOT A QUALIFYING PERSON.

BUT IF BOTH CONDITIONS WE JUST DISCUSSED DO EXIST.

THAT IS, YOU MUST HAVE PAID MORE THAN HALF THE COST OF KEEPING UP YOUR HOME FOR THE YEAR AND A QUALIFYING PERSON MUST HAVE LIVED WITH YOU IN YOUR HOME FOR MORE THAN HALF OF THE YEAR.

THEN, YOU MAY CHOOSE THE HEAD OF HOUSEHOLD FILING STATUS.

FOR MORE INFORMATION ON THE DIFFERENT FILING STATUSES, PLEASE SEE PUBLICATION 501.