Other financial discussions

An ITIN will not be accepted for a qualifying child.  See IRS FAQ Does my qualifying child need to have an SSN? states:

A qualifying child must have either:

• An SSN that’s valid for employment and assigned to them before the due date of your 2019 return (including the filing deadline postponement to July 15 and an extension to October 15 if you requested it); or
• An ATIN.

An ITIN won’t be accepted for a qualifying child.

First stimulus check qualifications (assuming you meet the income qualifications)

Generally, you were eligible for the first Economic Impact Payment if you are a U.S. citizen or U.S. resident alien, you  were not claimed as a dependent of another taxpayer and have a Social Security number valid for employment.

Second stimulus check qualifications (assuming you meet the income qualifications)

Generally, if you’re a U.S. citizen or U.S. resident alien, you may be eligible for $600 ($1,200  for a joint return), if you (and your spouse if filing a joint return) aren’t a dependent of another taxpayer on a 2019 tax return, have a social security number (SSN) valid for employment.

Check the Third Stimulus Check Calculator for see if you qualify for the stimulus.

My understanding of the 'mixed status' rule change had to do with one spouse on a jointly filed tax return having a SS number and one having an ITIN.

Under the initial rule, when the first stimulus payment was issued, if one spouse in a married filing jointly tax return does not have a Social Security number, neither spouse can receive the stimulus payment.

Under the rules of the second stimulus payment, if one spouse does not have a Social Security number, the spouse with a Social Security number and the qualifying children with a Social Security number will receive the stimulus check.

The December COVID-19 Relief Package retroactively changed the rule for the first stimulus payment to be the same as the rule for the second stimulus payment.