Are you asking about the kids that are 6 years old, or 26 years old?  We don't punish children for the crimes of  their parents, so the adults are safe.  If the youngsters are being claimed on a return filed by someone without a Social Security number authorizing employment (which, technically, can be issued to some people who have applied for adjustment of their immigration status) then there is no $500 payment for them.

The citizen spouse would qualify for $1,200, and citizen children on the spouse's return would qualify for $500, subject to the income limits.