W4 Withholding - Non-resident spouse with ITIN

You will still file as married - but it will be your choice to file Married Filing Separately (MFS) or Married Filing Jointly(MFJ) unless you qualify to file as Head of Household - see Head of Household filing status with Nonresident Alien Spouse.

The primary differences between MFS and MFJ will be that filing jointly will give you a higher standard deduction but will also require you to make an election to treat your wife as a U.S. resident for tax purposes and include our wife's worldwide income (if she has any).

If you made the election to file jointly and treat your wife as a tax resident for 2019, then you will need to continue to treat her as a resident or revoke that election.  (Note: should you choose to revoke that election, she can never make that election again.)  

If you will file MFS, then you will choose "Married. but withhold at higher single rate" on your Form W-4 for withholding. Otherwise, elect married.  

If your children have U.S Social Security numbers, they will still be your dependents for tax purposes, if you provide for more than half of their support.