Who is Eligible to Sponsor a Parent?
If you are a U.S. citizen and at least 21 years old, you are eligible to petition to bring your parents to live and work permanently in the United States. If you are a lawful permanent resident, you are not eligible to petition to bring your parents to live and work permanently in the United States.
So if the kids are U.S. Citizens and over 21, the parents are home free. That's the law.
Is this a great country, or what?
Maybe the father is too scared of "people hunting migrant people along the border" to apply for citizenship - can you answer the hypothetical question now?