I have a concern about whether my youngest son is qualified for the child tax credit
Based on my understanding of your post, your youngest does qualify for the child tax credit. He did live with you more than half the year. There's nothing in the IRS requlations that say he has to live with you "in the United States" for more than half the year. Without question, he lived with you for the first 17 days of 2020.
Then you state he stayed behind "vacationing" with other family. That time vacationing counts has days having lived with you, since after the "vacation" he returned to you where you live now. That vacation is considered a temporary absence, and does not count against you.
