real the statement closely, it says 'THE parent'. It would have been better to word it 'A parent'.
when the first stimulus was approved by Congress, unless both parents had SS#, there was no stimulus paid.
but that changed for the 2nd stimulus, retroactive to the 1st stimulus. As long as one parent had SS#, then that parent and the children with SS# were eligible for the stimulus; the parent with the ITIN remained ineligible.
So it would not surprise me if you received both stimulus payments for you and both for your children; you wife is ineligible.
also that link says it doesn't impact your GC.
